There aren't any recorded examples, because if you get banned BattleEye refuse to provide any evidence, tell you why you were banned, or even entertain the notion of an appeal. They literally just say "You know what you did, and we don't ever make errors!"
Bear in mind theres a forum post somewhere where one of the DayZ devs or forum admins says you can get banned for killing people in the debug forest that the game spawns you in sometimes. And nowhere in the game does it inform you of this, also there's nothing to stop anyone else who is also spawned there from just shooting you in the legs (or shooting around you, or just wounding you, etc), forcing you to defend yourself. The only negative thing of shooting someone in the debug forest is you die.
And thats just relatively innocent actions. To play devil's advocate for a moment:
All the people who run scripts to spawn guns/helis/turn everyone into dogs, whatever. They get banned too (I would assume, they did that huge ban wave a while ago because of this?) but all they're doing is running scripts in the game, which the server runs and pushes out to every other client because of the way ARMA 2 is designed. There's still nothing stopping anyone from doing this, and while it's kind of a dick move when some invincible teleporting thermal sniper dude murders you, it's nothing that can't be solved by just banning them from a server. The only reason it's such a big deal is because DayZ has this permenance thing about it (permenance in an alpha experiment that you don't get to complain about when bugs kill your character, no less).
To take it a step further, if you were paying to host your own DayZ server, and decided you fancied flying around in a chinook to pick up your friends so you could all kill zombies together, battleeye could flag your spawning it in and ban you and you'd not only have no explanation but also no recourse for appeal. (granted I assume that server admins probobly don't need to use these specific scripts to spawn stuff, and battleeye supposedly just checks for snippets of specific scripts which it flags as bannable). But you're still in a situation where on one hand this alpha experiment mod is losing people their CD keys, and on the other hand you're not allowed to take it seriously or express any problems with the direction the game is going. It just seems really inconsistent to me, though I get that impression from Rocket's handling of the mod in general.