Customer (name blocked for privacy);
It is unusual for an independent repair shop to be unable to fix a problem with anything driven by the serpentine belt. Obviously something broke that was driven by the belt that cused it to derail and leave you stranded.
A round corrugated disc could describe parts of several different components; it could be part of an A/C clutch, a serpentine belt tensioner, an idler pulley, or possibly a harmonic balancer. From the description I can't rell you for sure which component failed; but if you have a part in your hand, a quick peek under the hood should reveal where it came from...
It sounds like the place you went to for help either is ill trained, or doesn't do much repair work; almost any independent shop can handle repairs of the type needed here. A dealer visit is not necessary unless the component is covered under a factory recall or a dealer warrranty that would entitle you to a free repair; you may want to ask the shop you were at why it is that they are suggesting you go to the dealer for repair.
I hope this is helpful; if so, an accept would be most appreciated! thanks!