Balk?

[BSBAL18]

2 outs. R1 at second, R2 at first. Right handed pitcher.

Pitcher comes set and R2 takes off for third. Pitcher raises left leg and steps towards third as a normal pickoff move. During this, R2 stops midway and pitcher fakes the throw to third but DOES NOT disengage the rubber with his right foot. So he looks a little silly with a step towards third with the back foot still on rubber.

Coach flipped and was dancing around yelling balk. I did not call a balk because the runner left before the pitcher started to home and he legally made a move to third base AS A FIELDER. I read a post on this forum stating this scenario does not warrant "throw to unoccupied base is illegal" because the pitcher has the right to make a play on the runner. ( the post was within the last 4 months but it may have been deleted or archived).

Was it a balk or not? R1 ended up getting tagged out, inning over.