Those points aren't necessarily in disagreement. I've known a lot of people who thought they were ready for the next level or two steps up but weren't. So they went from an A+ IC somewhere solid to a C- "director" at a startup as soon as they got the chance.
(disclosure: former PM, current Head of Product, have almost certainly made this class of mistake)
The worst heads of product I've had could all answer yes. None of the best could.
Do you actually seek this out?