I think this make senses in the 'grand scheme of things' but on a granular scale, it probably does help with (an arbitrary figure like) 1% difference and that 1% probably matters at this level.
I can imagine if you've played the majority of your career on 'one side' then adjusting to another part of the pitch will affect e.g how you receive the ball, how you open your body up, what's your natural peripheral vision/eyeline sight, what's your stronger standing foot, how do you shield a player going down the channel and your sensibility for looking over your shoulder etc. It really depends on the player but all in all, I do think there's a reasonable deduction to say 'he can play on the xyz side but is he the most natural, comfortable and/or experienced at it?'.
I know it's a different proposition but it's like looking at wingers and fullbacks and seeing how comfortable they perform their roles on the other side. It's not really that straight forward.
Overall though, agree on the bolded.
Out of context/for shits and giggles: I usually play at the back in defence in 5/6/7 aside and for some reason, I'm most comfortable receiving the ball on the left but I'm best shielding players down the line on the right