He's a good friend and I thought he would do something about the problem, but he keeps bringing the same crappy guitar and getting bad results from it. I have mentioned to maybe use a different guitar, but then out comes another crappy guitar that has some issue with it.
Look, it seems like this:
1. He couldn't care less if it's in or out of tune. He goes for the poser, and wants guitars that looks cool instead of sounding cool. Period.
2. He uses thin gauges strings 009 or 008 that goes out of tune just by STARING SHARPLY at them.
3. He still is too rudimentary in both playing, and setup. Some cheaper guitars will not be setup ever due to constraints and cutting corners in production, as you said with strings getting caught on the fret sides, which has nothing to do with set up, but poorly made fret filing and levelling. It's mostly when he bends and do whammy bar things.
4. Some guitars, even high end ones, depends on traditional design, wood, and construction principles, and goes out of tune no matter what. Gibson SGs anyone? Tune it up perfectly with a proper accurate strobe tuner and then do this: Do a string bend up at the 12th fret on the B-string or G-string BUT DON'T PLAY THE STRING. Play the low open E string and take a good luck at the tuner. The bending of that other string makes all of the guitars soft wood, and nut be compressed, and it acts just like it had a floating tremolo on!!! It's due to that they make all of the design to weak, and faint, and is prone to headstock breaks, and the wood of the neck. If they only "upped" the dimensions all around with even one millimeter, such things would stay clear. You can do the "neck wiggle" with any SG, and see if anyone stays in the same position after you wiggled it with your hand. I e grabbing the headstock to produce a vibrato. The strings gets caught in the nut, and the lot of the neck doesn't ever go back in the same state, leaving it out of tune. The Les Pauls are much much better at it. Strats, and Teles too with a bolt on neck. You can do this trick on a Strat too, provided that you screw down the bridge tremolo block totally flush with the body so it doesn't react to anything done to the strings. It doesn't behave like that.
I've even seen one - real Gibson SGs, not cheap copy - changing the already tuned up open strings, while tuning up another string. The whole neck and instrument, and nut, reacts like it had a floating tremolo system. One strings increasing in tension is enough to pull the other ones out of tune, regardless of that you've already tuned them up. Which means you can't play a number through live, if the high E-string should snap because it throws everything else out of tune, just like it had a floating tremolo. I've even played MusicMan guitars that does this, can you imagine that?! Some does, some don't.
Now this is on original brands that costs major dough. Think for yourself what happens on cheapskate copies of them where they skimp on even more things.
5. It's not the guitars of his that needs to be changed out. It's him.
Really. I would, regardless of him being a friend. If not, I would jump ship with all other excuses, there is. Nothing to write home about.