I also put on a friction sway bar and have 0 sway issues. The shop is correct, the frames on TT of that size/type are not really ment to handle a full-on distribution hitch/sway configuration. I think they could end up bending the frame. These TTs are designed to be pulled w/o one due to their light weight. Picked up my friction bar from CW on sale for about $50.
*Currently trailer-less but shopping
07' GMC Envoy w/ P2 controller (current TV)
88' Chevy K5 Blazer (soon-to-be TV)
74' VW Superbeetle (1303)