Foul tip? Direct?

[TussAgee11]

BigUmp brought up a point in the flow chart about foul tips being "direct from bat to catcher's mitt".

Last night I had a play that brought this into question. 2 strikes, batter tries to get out of the way of a pitch on his hands. The ball hits bat (either the handle or knob, definatly not the hand) and richoches back into the catcher's mitt. The ball did change angle's due to contact with the bat.

Well at first I called foul, because I thought there was no way this ball was caught (white uniform on the batter, lost sight of the ball), then the catcher turns around and has it in the heel of his glove (a very nice play by him).

I called the batter out.

The pitch was direct from the bat to the catcher's mitt. It wasn't direct from the pitcher to the catcher, but that isn't in the criteria. When is the "direct" rule violated? Was it in my scenario?

Thanks.