Weirdness, I am Polish and, for obvious reasons, my most recent stays have been disproportionately domestic. I cannot remember the last time I was asked for an ID - I guess it was indeed in CS. I believe Italians had a weird fetish of asking me for my IDs, the others were fine with me presenting the LCAH / ALL card. Outside of the EU, I remember being ID'd regularly.
THAT SAID
I bought stays with both points and cash for others, and even if they were ID'd, neither was their stay denied nor an eyelid batted, and I even got my nights credited for those.