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Yes, the CA could have put it on his CR. CRAs do not verify the information given them.
Wrong and inaccurate information showing up on a person's CR happens all the time. It is left up to the consumer to prove it is not their account.
I went through a very similar incident a few weeks ago. Got a bill from a CA out of the blue for $600 on a Dish Network account that I supposedly owed. I was very frustrated as I hadn't used their service for about 3.5 years.
I will spare all the details, but talked with the CA rep who believed it to be an error but her hands was tied, and then spoke with 2 Dish Network reps with no real results. Finally I found the email to the CEO of Dish Network and sent an email documenting out all the facts and records of the phone conversations I had, and how if I had owed them money they failed to ever contact me prior to 3.5 years later. I went on to say they had obviously made a partial mistake as they owned up to and offered a partial credit, and I needed them to admit the rest of their mistake. My final closing remarks was this was beyond the SOL anyhow.
Within the next day or two, I got an email and phone call (on new number) indicating all charges had been removed from my account and all negative information from my credit reports.
I felt very fortunate to have it resolved. My point being, after learning it was yours then your uncle should have let you handle it. We don't know the specific details of your situation, but based on my experience I believe it was possible you could have gotten it taken care of without paying them assuming it was a true mistake on XM's behalf and it was put in front of the right person.