If {diochan, artful beauty} is equipped with {swift foot boots} can my opponent target it? Because don't I technically control the ability?
No, your opponent can not target it. You are actually giving the opponent a chance to target. They don't actually control the creature ability.
702.11b (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=702.11b): "Hexproof" on a permanent means "This permanent can't be the target of spells or abilities your opponents control."
I don't think hexproof would help. Since Diochan is the one doing the targeting.
Quote from: ThassaDevoted on November 11, 2013, 03:48:17 PMThey don't actually control the creature ability.
That would mean they can target it, not that they can't.
You control the ability so hexproof does not protect it. Just because your opponent chooses a target does not mean they control the ability.
However, if you're seeing if what happened in Friday nights was legal, it was {Lightning Greaves}.
Since it says they choose, but since you control her and her ability on the stack, you'd have to equip her with {Lightning Greaves} to do any good.