Hello XXXXXXXXXXXX,
If the complete exhaust system is rusted to the point the new muffler cannot be welded or clamped to the existing system, then yes it would need to be replaced from front to rear.
They may be wanting to prevent a possible "come back" where the service they provide would not last for the warranty. You may be able to talk with them about installing the muffler and voiding their warranty (in case the muffler were to break loose in the next few months). There would be a risk of the muffler leaking and the remainder of the system would have to be replaced at that time.
Regards,Jason
ASE Advanced Master Technician
16 yrs exp, Auto/Diesel Associates degree, ASE Master w/ Advanced cert, Saab Master and BMW level 4