Scenario: I'm cruising Thingiverse, and I find the awesomest thing. I NEED THIS IN MY LIFE. I download it, print it, and for whatever reason, it doesn't work quite right. OK, no big deal, I'll just download the source because the maker was so kind, modify it ever so slightly, and I will have the most awesomest thing evar!
Several hours later, I realized that I could have designed it from scratch in a software that is way more user friendly, deterministic, simpler, etc.
And then I do redesign it. From scratch. Maybe taking a measurement or two from the thing, or something related to the thing. And I refine it, and it turns out better than the original was.
Did I make a new thing? Did I only draw inspiration from the previous thing? Did I make a derivative work? Using Thingiverse's terminology, did I remix it?
I'm looking for some canonical guidelines to refer to for the US. Thingiverse can be an example, but god answers should not be limited to Thingiverse, nor my specific example.
I ran into this issue while trying to print out a case for a Raspberry Pi Zero. I'm not done redesigning it, but I've been wondering how I could share it on Thingiverse, and if any restrictions from the original model's licensing might affect me when I post my thing.
When you remix, either by modifying the existing CAD files (STL or sCAD or whatever), or by rebuilding essentially the same item from scratch, that is a remix and subject to whatever restrictions the original author put on his work.
So the critical issue so far as copyright is concerned is whether the output is a clear copy or remix. No different from taking someone's novel and rewriting it using Notepad++ and LaTeX instead of the original Microsoft World.
Now, when remix or reuse is allowed by the originator, it is still incumbent upon you to provide proper attribution, just as you would provide footnotes and bibliography so as to avoid plagiarism in a research paper.
All that said, you are free to do whatever you wish in "the privacy of your own home" (IANAL and laws vary by location, but the chance that the copyright holder will track you down because you have a widget in your bedroom are nil). You can't publish or sell, of course w/o permission.