There's no doubt that many SGs are more flimsy than most other models of guitar. Strength-wise, compared to a Strat or Tele the SG doesn't get near them, but it should stay in tune without any problems. I would suspect nut or stringing problems before anything else if there's a tuning problem with an SG. If it's a situation where the whole thing goes out of tune after a few bends on the B or G strings then I think it might need a truss rod adjustment, or maybe it's a dud?
You may be referring to the neck stability test (?) - pick the low E open and let it ring, then at the same time bend the high E up 1 step at the 12th fret, does the low E go flat slightly? It probably will, and this is just a fact of life with many SGs, and lots of other guitars as well. It's very likely that only guitars with quite fat necks, and/or pretty strong fully dried wood in thinner necks (and both properly set-up) will not exhibit the de-tuning when tested in this way.
And, as you already know, never drop an SG!