Happens all the time. I once tapped another car driving into a sunday league football ground. There seemed no damage and the occupants played in the match. But of course months later I got a letter saying how they'd had to have time off work qand were suffering from whiplash injuries/sleepless nights and needed to get cleaners in to do housework, needed a holiday in the sun to recover, etc, etc. It's frustrating and annoying but you can't do much more than refer it to your insurer.
It's up to the insurer whether they fight it as it's their money that will pay the claim. By all means tell the insurer what you think but if the other side has medical 'evidence' (from doctors employed by solicitors who make money from this sort of thing) then they may not be able to defend it.
It's always a good idea to take a photo at the scene to show there was no damage but that wo't mean much if they have medical evidence and garage evidence