Defence lawyer Thomas Ross said he was “not entirely surprised” that Bain had informed Swinney about the case.
He told BBC Scotland News: “It is expected that the first minister may be asked questions in relation to proceedings so it’s entirely right that the first minister should know the stage at which proceedings have reached.”
Ross also said a delay to the preliminary hearing was “quite normal”, especially in cases where there was a lot of paperwork, and said nothing about the case so far had been “murky”.
He added: “The vast majority of cases have no political aspect to then whatsoever and most of them are postponed at the first preliminary hearing so there’s nothing surprising really about it.”
The COPFS said previously that Bain and her deputy, Solicitor General Ruth Charteris, were not involved in the Murrell case because it involves politicians.
A spokesperson for the COPFS said: “The lord advocate provided the first minister with an update to ensure it was understood she was not involved in the case, that it was active for contempt of court, and therefore it should not be commented upon.
“This message was sent formally after the indictment had been served in order to form part of the record and ensure transparency in due course.
“Once an indictment has been served on an accused it stands to become public at any point.”