You are correct...to a point. The oil based paints MUST HAVE a primer used before paint is applied. This is an extra 2 steps (two coats is always recommended) that your painters may not have included this in their quote.

If your painters aren't happy with this idea...they have most likely had bad experiences with their own approach to painting latex over oil. This can be a tricky thing. All the prep and all the right steps can still lead to bubbling and pealing.

Thanks for the information. It's been a quandary for me. Perhaps I will do a 'test' (with all the prep and such, of course) on a hidden part of the wall (behind the fridge) to see what happens.

we clean the walls first patch any holes then prime and then top coat with latex but we have also painted over oil without primer without any problems

We used the latex paint and it went on/stayed on just fine over the oil.