Ball/Strike count confusion

[donj]

Had this happen to my plate partner and wasn't sure how to handle it either. Pitches go like this:
1. Foul tip strike - not recorded on indicator
2. Ball
3. Foul Ball
4. Ball.
Count should be 2 & 2 but recorded as 2 & 1 and plate ump tells batter count is 2 & 1.
5. Called strike.

Opposing coach comes out of dug up and tells the umpire that should be strike 3. Explains the pitch process and then the plate umpire tells the batter he's out on strikes.

Batter's coach gets' upset and talks to the ump that he can't change his count and call his batter out because he messed up. Ump stayed with his decision and the batter was out.

What's the ruling on this and if there is a reference in rules/case book on this, please list. I can't locate one.

Thanks,