Sounds like a CS PhD! hahaha (maybe Math?)
I want to preface by saying that for most work that goes on in Silicon Valley a PhD adds nothing.
I know what you're talking about.
However outside of SV there are a lot of places where that's simply not the case. What you have is basically a cross disciplinary collaboration where you just don't have the educational background nor the expertise to do the engineering yourself.
The resentment your describing is really the same resentment you can feel towards your boss -"All he does is tell us what to do. He's not in the trenches like us!" - and it's directly related to the amount of mutual respect. In essence, how hard do you feel the other person is working relative to you.
Your description of your coworkers seems to indicate that you didn't feel like they're pulling their weight, and that's definitely a big problem.
I've heard second hand that in the valley there are a lot of incompetent PhDs that use their educational background as leverage to slack off. People will often hire graduates solely based on a degree thinking that if someone has a Math PhD "they're smart, they can learn on the job, and they'll contribute in some magical way just by being there". But actually these guys have just spent 5 years in poverty getting an advanced degree and don't want to be a code monkeys with a bunch of fresh out of college 21 year-olds. And, oh yeah - reality check, no one cares about their degree in abstract algebra.
9/10 of these PhDs are crappy engineers and 9/10 times they are thrown at problems they don't really have a background in (so they can't even be crappy and regurgitate equations they're memorized).