Why would the BBC wish to settle if he has sent threatening messages which might put him in breach of contract and therefore gross misconduct?
For the BBC itself (even if it's another part of the BBC) to say within its capacity as a journalistic organisation that the message was threatening it must have passed a lawyer.
To think it hasn't is insane from two points of view - one it would undermine the BBCs journalistic integrity and two it would leave it vulnerable to get sued by the presenter.
On top of that the BBC can't really have the optics of giving licence payers money to someone doing this in a settlement. Not at this point. It will look like a cover up.
So the BBC will be hoping for a resignation with dignity (well what's left of it).
Even if he's lawyered up, what does he hope to achieve? He's not going to save his career is he? His career was built on a certain 'suitable persona' reputation. Now he will just be followed by jokes.
The fact here he's not going to get away from is that he's a married man on a dating app. So even if there is no illegality, his reputation has gone to shit and he isn't going to be able to deny how he met these two people.
The BBC can't have a man in his job. It just doesn't work. And the same goes for rivals. He will have to look for alternative roles regardless. And he can't blame the BBC for that.
Let's face it there will be someone turning in their grave. And that idea/imagery is exceptionally damaging to the organisation.
I suspect the devil will be in his contract over his conduct and bringing the organisation into disrepute. If the contracts are what they should be, he has a real problem that lawyers are unlikely to be able to be able to fix.
The lawyers can only fight off more serious allegations - ones suggested of a more sexual nature.