That is an excellent question Gretchen and perhaps for us working in the asian market the best way of answering that question is referring to the very origin of the TPS (Toyota Production System) in Japan.
In asian countries where the only constant is change, design thinking is not a choice but a matter of survival. In this environment the speed at which companies need to learn about their customers and markets from all over the world is such that most companies take design thinking into consideration naturally from the very beginning.
The values we have witnessed are very diverse ,since the design thinking process is based on discovery, however in general we could point at resource savings, adaptability and forward thinking as the most valuable to us.
Companies start up with a mindset of adaptability and try to see opportunities and not problems. If the housing market is slowing down 'perhaps' it is just the right time to enter the refurbishment business and scale up again.
From the very beginning after a new assignment, a combination of redundancy and minimum viable product (MVP) is set in place. This practice is extremely responsive with feedbacks from the client. A series of options are developed to test the waters and learn what the client is really looking for.
There are dangers in being extremely responsive. As Henry Ford said: 'if you would have asked people what they want they would have told you faster horses'.
We try to be responsive but the best practice is to find a way of translating that feedback into actionable metrics.
The key is to let the customer take the lead. Take the leap of faith to start a journey of discovery and a long term relationship. Something that sometimes is really difficult back in the west.
The game changer is to accept that the company will not decide what it is to be made, produce or designed, and take in that we are just facilitators that serve of guidance for somebody's else vision and desires.
I hope that is answering your question.
Look forward to your questions or comments if any.

Gretchen,
i love Tony's response and I will exapand a bit more.
First, I do not think thats its a fad but i do think that its common sense and as such its sold in an overly formulaic way. In this regard, as happens all too often, folks are looking for the magic product develop, marketing and innovation bullets when in fact really great thinkers are holistic thinkers, like a Ford, Edison or a Jobs, who seek to understand their world and opportunities first, to allow for a contexted abstraction of needs and then package contexted need sets as abstracted product ideas. This abstraction eliminates paradigms, such as the affirementioned horse analogy. People want to get from A to B safely, within a certain time frame, under a certain circumstance, etc... versus i need a faster, healthier horse. Defining a time frame thats something a horse cannot do by example forces different thinking.
To your question then, I will argue that great product design has always existed, but maybe through design thinking in part more folks are now more aware and can be better but the brilliant minds will always be there and do not need it. in the end its common sense where context is they key, not a training class.
In I and my colleague's world where we do transformational work, we codified the latter practices or really principles of approach into what we call Adaptive Innovation. You can see the paper on my LinkedIn page or at our Elemence.net website.

Hi Gretchen,
I think your question touches on one of the most important things in business, which is a firm's culture. As the great Peter Drucker said, "culture eats strategy for breakfast".
You're on to something important when you ask if people see design as "making things pretty", because they do. Design thinking is hard for a lot of people to understand because they get hung up on the design instead of the thinking.
I've worked with clients in both the private and public sectors, but I haven't seen much of a difference in how they approach problems. They look at things through the frame of their culture first. That often gets in the way.
From what you describe, your team is already primed to use design thinking to help make their products better. It works! They just don't have the language or the culture yet to do so. I bet if you went to them and said something like "let's adopt agile methodologies", you would get a lot of confusion and resistance. Those are confusing words they don't have a reference for.
I've seen lots of firms be resistant to trying new things for exactly those reasons- new jargon, techniques, and processes sound like they will require a lot of cost, training, and time that they can't afford.
It sounds like you are already changing perspectives, keep it up. If you have some control over the process by which people request your work, you can make simple changes to push the team further along. Do your work processes and forms make UX and ADA issues mandatory to address before proceeding? If not, why not? Go ahead- you definitely have my permission.
Keep chipping away like this and soon you will most likely see an "aha" moment where others are inspired to think about process as well.
Good luck!

As designer, I believe Design Thinking is a great tool if used correctly by a designer or at least a designer should supervise the whole process. There is no great design thinking without a real designer.

I have an article explaining why "Design Thinking is not Design" at my LinkedIn

I will mention some of the main points of the article here:

THE NEGATIVE SIDE OF DESIGN THINKING (DT)
I believe many businesses and schools have this mistaken view that a single DT creative brainstorming in one afternoon would solve all the problems of a global company in several areas from design, engineering to management. Nowadays, companies want innovative solutions quickly and at low cost, and it seems that somehow, the DT has filled this gap. 
The expensive, complex and time consuming process demanded by the “traditional” design, was transformed into a cheap, fast and without major complexities process within this superficial frame of DT.
This perception of DT displays the Design Profession as something that can be practiced by anyone, without the guidance of a designer.

THE POSITIVE SIDE OF DESIGN THINKING = DT
On the other hand, DT led to a greater ‘right or wrong’ understanding of Design and its worldwide popularity in business schools and corporations, but especially at the business environment where with DT they began to realize the importance of design for their survival in the wild global market. Therefore, Design gained unprecedented visibility in its history with DT due to thousands of books, lectures and articles on the subject.

Arguably more Design happens in the world because of the DT, and this is very positive and necessary.

All participants are co-designers? Sorry, but no!

The participation of other co-creators (and not co-designers) is very welcome and much needed in the design process, but only the designer has the experience, knowledge to filter and transform these insights in the desired end result.
You cannot let the final design decision for the participants, or transfer the design to the co-creators, therefore weakening the designer and the final proposal. This decision should be made joint with the designer, who will select the best proposals and will carry it forward.
So it is also important to clarify the role of the participants and the DT, how they participate, the outputs of the process and next steps within the Design process and not naming wrongly the participants as “co-designers”.

Thanks to all contributors you have said it all.
Design is more than design.