I have two sets of originals here and I was looking at them tonight. Looks like there are short thin studs cast into the outer chrome trim which get crushed over the plastic shell to hold the two pieces together. I will probably have to gently grind away the "mushroomed" tops of the studs to get the grills apart. Maybe yours had been apart in the past so yours just came apart when you took them off?
Anyway, thanks for the tip on the plastic welder, now I can get those cracked shells fixed.