Don't mention that you are using eCart, that shouldn't matter. Concentrate on the XML you pass to them and the XML they return to you.
Go to the debug page that we have added and view source. There you can find the XML Request and XML Response from UPS.
Just give that to them and ask them why it is returning a different rate than their site and ask why it isn't working with negotiated rates purely from an XML perspective. Once we understand what is wrong with the XML then we can help you make the necessary changes from within eCart.
I can't tell you why it would be returning different rates, but they should be able to. Once we understand that, then I can help you make any necessary changes.
If you have a hard time figuring out which XML to send, then send me a copy of the source in the private area and I'll pick it out for you and show you what to send them.