Should stuck on mouldings on doors be replaced with new ones after spraying?

There is currently nothing wrong with the old ones, but my bodywork man says that if he just puts the old ones back on they'll likely not stick properly and will eventually fall off again, and he won't guarantee them unless I put new ones on, which are working out very expensive.

I'm wondering whether I should believe him or not, and if I should take it somewhere else to get fixed.