The head of the corporation's flagship Radio station praised Moyles's abilities as a broadcaster, and said that while Wednesday's programme "wasn't the best" instalment of The Chris Moyles Show, he did not consider the presenter's behaviour to have "crossed a line".
Parfitt said: "[Moyles] is a very gifted broadcaster. Occasionally, and it is only occasionally, he steps over a line that I have.
"And when he does that I'm absolutely there to make it absolutely clear to him where those lines are. It's kind of part of the nature of what he does, living his life in one sense out on air. He's almost bound to push at those barriers on occasion.
"I kind of made a judgement [about Wednesday's broadcast], did it overstep a line that I have for Chris? And I judged that it didn't.
"It was a lively programme - it wasn't the best Chris Moyles programme I've ever heard."
Parfitt added that he had discussed the situation with Moyles since the broadcast, but that he considered rectifying his payment issue to be top of the agenda.
Last week, the BBC's head of network radio Tim Davies said that Moyles's listeners understood him to be an outspoken character, and that the presenter's tirade was not "utterly inappropriate".