I know arguing terminology is fun, and, he probably didn't say it correctly in the videos, but his point was, I think, that what is often called phase, particularly in plugins, is actually polarity, which is just what the link shows. They are, of course, not the same thing, but phase is what the button says in my DAW!
It does seem like monitoring in mono and flipping polarity is a pretty quick, painless, and not uncommon check for drums.
Maybe a letter writing campaign to the plugin and DAW manufacturers that are abusing the phase term will get things set right...