Diochan, artful beauty

[Taysby]

If {diochan, artful beauty} is equipped with {swift foot boots} can my opponent target it?  Because don't I technically control the ability?

[ThassaDevoted]

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.

[Rasser]

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. 

[MementoMori]

They don't actually control the creature ability.

That would mean they can target it, not that they can't.

[Kaleo42]

You control the ability so hexproof does not protect it. Just because your opponent chooses a target does not mean they control the ability.

[lotrwk]

However, if you're seeing if what happened in Friday nights was legal, it was  {Lightning Greaves}.

[Vileo]

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.