Is it really Hertz fault that the tire went flat? I don't think you deserve any compensation for your trouble. That said, I don't think you should be billed for the tire, either. The way I see it -- there's three choices in this situation:

1. Drive the car around with the spare on it until you return it.

2. Drive back to Hertz and exchange the car after the spare is on it.

3. Pay someone to fix (or replace) the tire and hope that Hertz will reimburse you for it.

All seem fairly reasonable. Just decide which one meets your needs and don't let a stupid flat ruin your trip!