That phrasing struck me as oddly limp. They would have been “fine” for their president to stay At his job? That’s not exactly a strong statement of support. If my boss told me they’d be “fine” if I stayed at my job I’d be pretty worried.
If my boss told me he was "fine with me staying at my job", I'd take it to mean that they were fine with me staying at my job.
I don't think this press release (is it that?) does a very good job of dispelling the rumors that it wasn't entirely mutual, though. He ought to have said something like "delighted to have him stay".