Using "disk-only" rim (proper sidewalls) with rim brakes I have an unneeded disk wheel. The rim is "disk-only", but it has sidewalls just as though it was for rim brakes. The sidewalls are painted though and not machined. (I even suspect it's some older model re-labeled with "disk-only".)

What can go wrong putting it in a rim-brake bike? After a few first slowdowns, while I take some care, the paint wears off.

Can sidewalls of "disk-only" rims, while looking just like their old rim-brake-compatible counterparties, be significantly thinner or otherwise unsuitable for using with rim brakes? 

I'm looking for facts, not guesses or hypotheses (which I have more than enough myself :-) )
Facts are few and far between on this topic. It's best to assume that a disc brake rim won't have sufficient sidewall material for braking, and this is true the majority of the time.
There are some notable examples of rims where by all appearances, the extrusion sure looks exactly the same between the disc and rim brake versions. DT TK540s and TK540 Discs are one such.

However, there aren't very many current examples of rims like that, but there are a good deal with parallel looking sidewalls that are or should be assumed to be too thin to be a brake track.
The structural efficiency and weight savings of foregoing the brake track are very real, and now that disc brakes are the norm there's not a lot of impetus for manufacturers to eke more value out of an extrusion by using it for both disc and rim designs.