Which would suggest that the three months was certainly a possibility.
True, but the key word there is ‘possibility.’
All it says is that it cannot be longer than six months, there’s nothing to suggest that a shorter probation period would be likely. I’d guess the wording of that is intended to give them an option to end the probationary salary early should they suddenly want to start paying you more (eg, they wanted to keep you and you’d got a better offer somewhere else three months later).
If your boss is annoyed, presumably he’s onside with you. Do HR set salaries? If your boss knows he’s made a mistake (ie, you don’t have to prove anything), isn’t he able give you a pay rise earlier?