Is a weak battery a valid reason to reject a rented aircraft?
First off, you absolutely made the correct decision. As PIC/pilot you have not only the ability, but the duty to call off any flight you don't feel comfortable regardless of the reason. Your go/no go decision can be based off of anything and you should always be comfortable making that decision.

Now as far as the battery goes I can tell you I was in exactly this situation a couple years ago with a rented Piper Comanche. It was cold out and the start attempts completely killed the battery. The FBO (also the owner) decided to jump it using a start cart and got it going. They comp'd me about .25 hours since they wanted me to sit on the tarmac at 1200 RPM until the oil temp gauge came up (something that I would have done anyway).

I made the decision to go, but I also made (a rather poor) decision to board a passenger while the aircraft was running (at the direction of the FBO and because I was at an unattended airport to pick that passenger up). I don't regret taking the aircraft but I never felt comfortable boarding somebody with the engine running.

In this situation you probably would have been fine had you left, provided you were making a VFR flight in good conditions. If this were IFR I would say that it would be better to say "no-go". The only thing you would probably have noticed would have been the ammeter showing the battery charging, but it would probably have recharged the battery in about 30-45 minutes of flying.

The other question is if the owner should have comp'd you for this and that is a little harder. You probably didn't burn all that much fuel or put much time on the engine tach so I'm guessing that while it would have been inconvenient to the owner, you didn't make a lot of difference financially (maybe $20 at most).