If the debt collector ever had legitimate collection authority, then there is no prohibition against their reporting that fact to a CRA, even after the debt has been paid.
That is not to say that the debt collector would report a collection after they know it has been paid, as most debt collectors view credit reporting as a technique in promoting collection of the debt, and after the debt is paid, they have no real business interest in taking the time and expense to report their closed, paid collection.
The exception is if you get the creditor to terminate their assigned collection authority before you pay the OC.
In that case, CRA policy instructs debt collectors to delete their reported collection. That CRA policy is based on the fact that an unpaid collection that is terminated can immediately be assigned or sold to another debt collector, who can then report their own collection. The policy is thus intended to prevent two collections from simultaneously being included in a credit report on the same debt.
That concern is not present if the debt is paid while the debt collector still has collection authority.
