According to Dan Erlewine's Guitar Player Repair Guide, when adjusting the truss rod and action some sting buzz is OK as long as it's are not heard through the amp.
Is that pretty standard for most players? To leave some buzz if not heard through the amp and not affecting tone? This is my first venture into adjusting an electric guitar but I've adjusted several acoustic guitars where you want NO buzz at all. So this "OK to leave some buzz" thing is a different ballgame for me.
I've adjusted my truss rod for .010 at the 8th fret per Fender specs. Feels good, better than it was at .020. I like flat fretboards. I've left my string height at in-between 4/64" and 5/64" for now. Again that string height feels good, going a little higher wouldn't hurt I'm guessing, but would like to leave it be since she's playing very well. The only reason I would want to go higher would be to get rid of some buzzing that's not heard through the amp and doesn't sound is if it's affecting the tone. Before adjusting the truss rod there was some buzzing so it's not worse, didn't expect it to get better, but it's not worse.
So.. Some buzz is OK, back away from the tools? I'm letting my acoustic background be more nit-picky here than needed!
Or... Keep tweaking and get them buzzes out, you'll thank me later.