We used Alamo last August and luckily when they asked my husband for a credit card - he gave them his Nationwide debit card - in error! They accepted that fine and we were so glad as our car got hit 3 times whilst we were parked in 3 different places - Walmart's car park, our disney hotel and at Epcot! No one left their details - something I was really disgusted at.
So we said nothing and left the car and hoped for the best - but I was very worried!
Luckily, we didn't use the N/wide a/c anymore so when I got back I reduced our overdraft to the lowest amount possible, £50 and proceeded to close the a/c!
We didn't get any charges through, which I thought was very lucky. Our car wasn't terribly badly damaged, no wing mirrors hanging off or anything like that, but there were obvious scratches and dents that weren't there before! Luckily the car had got one dent already, so possibly that's why they did nothing!
So use a debit card if you can and do the same as me in case anything happens!!!