Here's what I think:

Chelsea asked for permission to speak to Frank, and Mel spoke to Frank to see if he wanted to have that discussion, or to dismiss it. Bear in mind that there may have been a clause in his contract to allow him to talk to PL clubs if he wished, we don't know. Either way, Mel would have spoken to Frank first out of courtesy or contractually, Frank said he wished to speak to Chelsea.
Thats it. Frank chose to leave after just one season - not just one season at Derby but one season of management. He went to a club where he was hero worshipped by fans but that had an owner with no patience and no loyalty to managers. It was an incredibly risky thing to do, and completely unnecessary. The job will be available many times in the future.
He made his choice, it hasnt worked out well for either of us but we've moved on and I'm happy with what we've got for now.