Yeah, I see what you're saying. But the assumption part is that the left channel is non-inverted and the right channel is inverted, thus your direction to invert the right channel. You're right in that they are now in correct phase with each other.

The distinction I'm making is that there's no technical reason that the left channel must be the non-inverted one. If we don't know which one is inverted, it's possible that the center channel signal will become out of phase with respect to the rest of the system.

I suppose that there's also a potential to get out of phase if using different amps as well -- if you're using one inverting amp and another that's non-inverting. The best way to assure proper polarity in this "mixed" case is to measure it.