From the sounds of it, Frost and Martinez went into the meeting with (generally) both wanting Martinez to return. But there was discussion about the path forward (looking at the transfer market, who the OC/QB coach would be, etc.) and Martinez wanted a guarantee that we wouldn't bring in a transfer. I don't know all Frost's reasons but if nothing else given Martinez's current medical condition and who might be hired as OC, Frost wasn't willing to give that guarantee. So Martinez decided to move on.
So there is quite a bit of room on either side to place the blame for who did or did not want him coming back. But it doesn't really sound like "Frost wanted to move on" is probably entirely accurate. More like "Frost wanted options."