Replacing balls in a match

I played a USTA singles match this weekend. We started the match with new balls, but after 6 games one of the balls seemed flatter than the others. I told my opponent, and he agreed that one of the balls seemed off.

We were at courts without a pro shop, and neither of us had another new can. I offered a can of balls (same type) that I had opened earlier that day for warmup. We could use those three or use one to make the third. He said no. He said without another new can, we had to play with only the remaining two.

What's the rule here? It seems like we should be allowed to sub balls when one is unplayable. It was a PITA to pick up balls after every point.