"Do not worry, you will not need to pay any money. I will make the correction on the account and the balance will reflect $0. This will remove the account from collection."
I can't say I love the phrasing here. I'm not sure you could make a strong case that the collection agent was stating it would be removed from your CR. I read it as "the account will no longer be in collection" which is true. I don't read it as a promise to remove it from your credit report.
However, that's just one snippet from the conversation! Hopefully elsewhere in the conversation is a more implicit reference to having it removed from your credit report. Collection agencies are a tricky bunch and they do this all day, every day. The consumer is at a huge disadvantage when speaking with them.
If collection authority is revoked BEFORE PAYMENT, then the CA is required to delete their report under CRA guidelines. OP indicated this was conversation with ATT agent, not a Collection Agancy.
Most Recent FICO 8 Scores EX601/TU580/EQ589 12/08/2017 Starting scores 553/485/543 08/25//2017 ~~~Credit lines~~~~ SDFCU VISA Secured $250 Discover Secured $200