It sounds like Spillway is full of a bunch of idiots. Definetly sounds like they dropped the ball big time and not Bowtech.
We are a Bowtech, Mathews, Hoyt, PSE, and Browning dealer and never have the problems with warranty work that you described. Even from Mathews.
I suspect that the "dealer" didn't either specify that it was a warranty issue or that Bowtech charged them the cost of the limbs but will credit the ammount back to the dealer upon return of the broken limbs. Almost all bow manufacturers will require the dealer to send back the limbs to them. Usually the manufacturer issues a return label in the box with the new limbs so the dealer can send back the broken ones free of charge.
Who knows, Bowtech may be having problems with this dealer paying bills or something and charged them for the limbs.
Bottom line is that you need to call Bowtech directly with your serial number, dealers name, etc... and tell them what happened. I bet they will instruct the dealer to refund you your money.
BTW, a string and cable shouldn't have cost you more than $70 for a factory Bowtech set.