It sounds like we were right, and that Americans say aged where we'd say mature, in respect of cheese. We'd call it an aging process too, as with wine, but the product would never be called that name. Does this suggest that on the right side of the Atlantic people have more respect for cheese?
Anyway mature cheese is stronger, more flavour, and you don't need to so much of it to get a suitable effect (egin an omelette).
A bit like people.
I draw your attention to this cheesy thread, with a tasty bit of verse in it. Cracking, in fact.