Not knowing how you wired it makes it extremely difficult to diagnose such as factory radio, adapters if any), it is also a bit confusing as to if the XM worked correctly before having service performed. However, since the factory has a right and a left input from the XM module, one would have to assume the left wire is no longer connected.
If the left wire is connected, then you could have a defective module.
As for the BCM, if accessories are installed and the installation messes up the factory equipment, the dealer can refuse to repair the item. However, the dealer better be able to explain fully how this new equipment has messed up the factory wiring or component.