Out of curiosity how much do you have in your budget to help pay tuition?
When schools ask you how much you would pay what was your response?
Also try and picture where the schools are coming from. Your child has never been in school, they have no way of knowing his level of education, or how he will behave. Coupled with no tuition I can see why they are hesitant.
Also, did your Rav really say that?
Sounds like a really suspect thing for someone with genuine torah values to say.