I would ask the other party to provide evidence of the damage caused to their car. If, in fact, there was no paint off or scuffing then what other damage was caused ie deformation of shape or damage to light fittings from the impact.
It would be unlikely that a 1997 Corolla bumper would have no other marks or scuffs on it so one wonders if they just want to use this incident to repair other damage. Be fair and honest about it but stick up for yourself. If negotiation fails you could lodge a claim with the disputes tribunal (either party can), which may make them drop a claim they can't support.