Nope. I actually developed two products for the second of the startups, which was the time period I was working on the side projects. The CEO (my boss) and I are still on good terms, and he knew about the side projects while I was working on them.
Startups usually fail because nobody wants what they're building, i.e. the startup should never have been founded in the first place. Certainly this was the case for this one: we were doing a platform for hedge fund algorithmic trading, but hedge funds are usually very resistant to running their code on someone else's platform, both because of lock-in/competitive reasons and because their code & algorithms are their crown jewels and they're very sensitive about running that on other people's infrastructure.
Maybe the principle is different though (not startup can bigco)... I did a bunch of side projects in school and at bigco before concentrating focus, so in a way we both went broad then had success going deep.
Just thinking out loud, I think we agree.