Apologies — the reason why that statement of yours was false was the “they might send in regular troops”
Firstly - Russia already sent in regular troops and has been sending them since February (the invasion and aim to capture Kyiv was by regular troops)
Secondly - Putin already had a partial mobilization and sent these conscripts to Ukraine.
Thirdly - there is no indication that Prigozhin is willing to give up place in Bakhmut to regular troops - he wants to prove that his Wagner group is better than the army generals.