I think that a lot of the confusion around Design Thinking is that it picks up related concepts like the hook side of velcro.
Co-designing is important, and works well with design thinking, but it is not design thinking (by my definition.) It is not a form of cognition, but it is a method (even a distributed cognition method) one can use as designer or as one who is learning to think like a designer. Design Thinking does not require it any more than design thinking requires you make a wireframe or do usability testing, but if you think like a designer, you will choose it when it will help you.
Back to chefs: you as a chef can offer a dish like you do at a korean BBQ place, and have folks assemble the food you’ve chosen for them, or you can do a prix fix where people get what you’ve decide they’ll eat, they you cook it, NO CHANGES. There is a time and place for each, and a wise chef knows which (and which suits her skills and style.)
Also, this is why I prefer Context to Empathy. Co-designing and workshops are great for bringing richer context to the problem. Empathy suggest you observe and have feels about the users. But maybe that’s just me.