Why argue the point? Just do what the manual says. What's so difficult about that?
Because all the manual can tell you is if that particular component inverts. But what counts is that the system as a whole should not invert, which as has been explained means that the total number of inverting components and inverted connections should be an even number (0 or 2 or 4).
As to "why argue the point," that was exactly what I was getting at in one of my earlier posts. Just get the overall system polarity correct (i.e., non-inverting), and then you don't have to worry about whether or not it makes a difference.
Regards,
-- Al