Can a tire that blew off a rim be safely used on another rim, and under what criteria?
I have a MTB where the tyres can simply be removed by hand once deflated.  The tyres are at 50~60 PSI normally.  But I can feel that they engage the clincher bead fine when inflated.

My guess is that your tyres never hook into the rim properly, and then overinflating found that area of the bead that wasn't fully seated.

As for the social side, as long as you clearly advise the recipient that you're giving them away, because they didn't stay seated properly on your rims then its the recipient's choice whether they use them or not.  I wouldn't want to see anyone hurt, but they'll be adults and can make their own choices.  Just help them to make an informed choice by sharing the history.