I'd agree you'd normally not use the root position if you're playing with a bassist (unless they're soloing), but whether or not I avoided including the root at all would depend entirely on what fit well under the fingers and "felt right" at the time. I never imagined there was any sort of "rule" around it...
There are no rules, which was exactly the point of my comment. There's no studying of systems to be had, because there is no system. I said "I always tell people attempting to learn improv and piano to 'play what sounds good and don't play what doesn't."
The particular sentence you quoted sounds rigid on its own, but when put into the context of my entire comment, it's clear that I'm not trying to give a hard rule, but a general convention. Like I said... you should play what sounds good; and don't play what doesn't
