Does age of asphalt shingles affect their resistance to hail damage?
Yes, to a degree.  Older shingles have lost much of their resilience and coating and what's left can often break easier or get knocked off easier.

New shingles can be damaged by hail but older ones are much more vulnerable.

You also don't know exactly what type of hail fell on your roof vs. one just down the street.  Hail can vary a lot in a very short distance.

The best thing you can do for your specific case is either to inspect the roof yourself of call in a reputable roofing contractor for an inspection.  I would NEVER trust someone who comes uninvited wanting to look at my roof.  Usually they are scammers!

You are correct, however, in that there is a limited lifetime and nailing capacity for roof decking.  If you've really had 3 roofs installed already you got your money's worth and it may need to be replaced.