Regarding them saying if it's not in the paperwork they'll do it, I'd want to know why a 10 year old car hasn't already had a Cambelt and water pump change and auto gearbox service!
They should be checking the history and telling you what it's had done. I'd like to think a 1 owner car has had the work done on time.
But with a 1 owner car you have to ask yourself why have they chosen to get rid of the car now. Sorry for sounding pessimistic.
Don't forget if you purchase it, you get 30 days where you can get a full refund for the vehicle, or the garage has to fix issues free of charge.
You could get an AA inspection or similar done on the vehicle. If the garage refuse then you'd have to ask why.