Agree; he's not harassing them, he's making a perfectly reasonable request to the benefit of both parties. I wouldn't hand in my notice without a firm job offer in writing either. And they must understand he can't give notice until he's got it in writing (inc. all details of the salary, pension, bonuses, holiday, etc. etc.).
When it comes to negotiating the package, you are in a much stronger position to do this BEFORE you sign. Once you are already with an employer you have to fit into their procedures and may wait ages for a review. Ask for what you want upfront ? if it's too much for them to swallow they'll probably compromise (I got my new employer to match my old salary, even though they advertised at 20 per cent less. They made it up with bonus/car allowance. So it can be done!).
HTH