I use to be a tire installer.
It is possible to put your tire on the computer and have it come back OK and not need weight.
HOWEVER
Normally when we put the tire on the machine or even before....we take the weights off. I mean you are paying to have the wheel balanced so why should I care if it is already balanced.
I am not going to check if it is already balanced. I am going to take the old weights off, put your tire on the machine and let the machine tell me where the weights have to go. Even if they go where the old ones were, what do I care? I'm just giving you what you paid for.
Your dealer may not have had the proper weights for your special rims, maybe he only had the standard weights for steel wheels and not the ones for soft mags.