What they said in the phone call is not relevant to reporting, and is thus moot as to any issue of credit report deletion.
An assigned debt collector who is only acting as an agent for the owner, and does not own the debt, is clearly authorized to report their collection to the CRAs.
If they do not own the debt they have reported, that tiriggers their requirement to so state in their dunning notice, which requires them to identify the owner of the debt. See FDCPA 809(a).
Additionally, statements made by a phone rep are not necessarily accepted by the courts as admissions of facts.
To err is human, and incorrect statements made by uniformed reps may not necessarily be held by a court to comprise an admission of fact when it is clearly shown to have been erroneous and beyond their authority.
When I mentioned consent, I was not talking about how they tell you that "this call may be recorded or monitored for quality purposes". If you did not expressly inform THEM that the call may be recorded, and if THEY did not give YOU consent for you to record them, then you did not gain consent for recording. I know, it's stupid, but there have been cases where the CA recorded the call, but was never told that the consumer was also recording, and the CA pitched a fit, saying they were never informed that the call was being recorded and never gave consent for the other party to record them. Generally speaking, if you tell them that you intend to record the call, they will end the call. Debt collectors today don't want to be recorded.
I've also known someone who tried to make the argument that their disclosure that the call "may be recorded" signaled their consent for a recording of the call to take place. Still waiting to see if the court will buy into that or not, but I can see his point. They cannot have it both ways---if they agree that the call may be recorded, then I cannot see why the call cannot be recorded. But that's just me.
The law is different in every state, in Texas where I live only one party needs to be aware of the call being recorded and that one party can be the one doing the recording.