I had similar years ago. Muppet drove into my parked car, my father saw it out of the kitchen window. He tried to drive off before my dad caught him. Admitted it there and then and swapped details. Next communication from my insurers was "hard luck – your word against his – he claims to have been fifty miles away at that time"!!
Had to push really hard to get my insurers to fight it because they had to engage a barrister. I guess this is more expensive than paying half of the claim? Same in your case I guess? It took 18 months before getting to court.
Ended up having to give evidence on oath as the judge wasn't happy that one of us was clearly lying. Turns out the other guy couldn't even read and was a hopeless liar. His witness was the fat slob that was in the passenger seat at the time of the prang. The clerks at the court suggested that they were fairly regular visitors for a variety of offences. Basically scum that see a trip to court as a good day out…
Yours sounds like arrogance on behalf of the other party tho. Just can't understand why people are so embarrassed to admitting fault – its not the end of the world is it?