Touch-Take Rule

The following question came up during a skittles game at a recent school tournament, and I would like to know the official answer:

Does the touch-take rule (the rule that says you must take an opponent's piece if you touch it) apply only if you touch the piece with your hand, or does it count if you touch the piece with one of your pieces?

p.s. I am aware that the mistake must be mental, not physical, and that the touch-move rule isn't supposed to apply to situations where the player didn't mean to touch the piece.

Touch Take is w/ piece

You must capture it with the piece in your hand if it is legal; if not legal, you must move the piece in your hand (if it is legal).