What I mean there is that if you tune a guitar to a perfect note, it will likely be off with itself somewhere. Some tuning "cheating" is often needed.
Let's say that you tune your A and G strings to perfect A and G notes. But when you shape a basic D chord, your G string pressed to the A note may be somewhat sharp with your open A string. No matter how perfectly the nut cut, the set up, the frets, etc., guitars have some kind of tuning imperfection that sometimes need strings to be cheated a bit sharp/flat to maximize them being in tune in general across the keys, fretted notes, etc. Some have to be retuned a bit to that they're in tune in certain keys. E.g., I have two that, despite being perfectly set up, need their B and G strings cheated a bit flat in the tuning if I'm playing in the keys of E and A vs the keys of G, C, D, etc.
So, yes, what Radiohead, like others, said above:
"Certain guitars don't sound as good for certain songs because of specific overtones, which may be caused by the exact position on the pickups, or overtones caused by the hardware or whatever."
This doesn't really have anything to do with tuning. And a chromatic tuner can tune to any fret you want. You don't have to tune to open strings.
I'm still completely unsure what having the tuning the "right way for the singer's voice" thing is.