Many (most?) companies will get you to sign some kind of NDA when you work for them. I've had interns work for me and had them sign them without problems. You say yours was heavy duty, so maybe there was something unique about it, but otherwise I don't see the problem.
I've never really seen any internet advice saying not to sign an NDA, either. The only related thing is advice not to try and get a VC to sign an NDA - but you are an intern, not a VC, and you are working for the company, not trying to get money from them. That's very different.
An NDA for a non-paid position where you give your time and effort to a company sounds like a bit over the top.
If they can't imagine a way to make you productive when you give your labor freely without needing legal representation yourself then they're nuts and don't deserve your gift.
Many (most?) companies will get you to sign some kind of NDA when you work for them. I've had interns work for me and had them sign them without problems. You say yours was heavy duty, so maybe there was something unique about it, but otherwise I don't see the problem.
I've never really seen any internet advice saying not to sign an NDA, either. The only related thing is advice not to try and get a VC to sign an NDA - but you are an intern, not a VC, and you are working for the company, not trying to get money from them. That's very different.
A NDA is very different to a Non-Compete.