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.
You're overanalysing something that wasn't the actual word used, and is an accurate word. We might all be a bit used to hyperbole, but the lack of it doesn't imply anything. Stop reading into it.
It's also the kind of thing you'd say if you knew that their heart isn't in it.
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".