I can confirm that one shouldn't trust all-purpose glue. Bought a tube of it a year ago, and out of about 10 times I've tried to use it, I don't remember a single one not needing re-gluing with something else later. All except your fingers of course - glue them, and they're sticky for weeks.
So well in fact that it can be used as an alternative to stitches. Medical grade cyanoacrylate is a bit different (less irritant) but in an emergency, the regular household kind can be used.