I've worked in private Christian schools for all of my career and my understanding is that private schools don't just get a lump sum of federal or state money that they can spend in whatever way they choose. Private schools apply for grant money and they may or may not get it. There are very strict restrictions on what government funds can be used for--for example they can only be used for things that will be directly used by the students. The government will not pay for any items that are religious in nature. In both schools I worked at grant money was most often used for technology-computers, projectors, things like that. The school does not include this money in its budget.
And there are some Christian schools--the really conservative ones--that refuse to apply for any government money, as they fear that they will be forced to comply with federal education requirements.
However, in both schools--the one in Saipan as well as the school I work at now in Ohio there were other ways that our school got funding via the government. In Saipan, the territory had something called ETC (Educational Tax Credit) which allowed businesses to pay up to $5000 annually of their business taxes to any school (private or public) instead of paying it to the government. For schools that were willing to do the footwork of contacting local businesses, explaining the law, and getting the businesses on board this could be a huge windfall. I heard (though I don't know if it's true) that at least one school (not a religious one incidentally) depended on ETC for up to half it's budget. This money could be spent in any way the school chose--in fact businesses were not allowed to dictate how the money could be spent. Though they weren't supposed to there were cases where a business would only donate ETC to your organization if you chose them as a vendor. For example, if you paid a certain carpet cleaning company to clean your school's carpet then they would also become an ETC donor.
Our school never included ETC in our budget because the money is not guaranteed. You have to solicit businesses every quarter and you can't always be sure they'll continue to give, but we did benefit from it, sometimes earning up to $25,000 or $30,000 in a year.
The Northern Marianas government (of which Saipan is a part) is basically broke so there has been some suggestion that they should eliminate ETC so that all of the tax money goes into the government coffers instead of being siphoned off to the schools. However the govt. is so pathetically corrupt, inefficient, and wasteful, that I personally think the money is better spent on ETC.
Here in Ohio we have what basically amounts to a voucher program called EdChoice, which allows parents whose children would have to go to a "failing" public school to send their kids to a private school instead, with the state picking up the tab. The state decides how much they will allot per EdChoice student and most private schools, in what I concede is a rather questionable ethical practice, set their tuition to match that amount so they can get the maximum allotment of EdChoice funds per student. (For non-EdChoice students, the school provides a "scholarship" that makes the tuition lower for those students who don't qualify). Unlike in Saipan, my school really does depend on these funds because our enrollment would be much, much lower without EdChoice. In my class alone, I think everyone except for two students were EdChoice students. Of course in this scenario, the state isn't being saved any money as was suggested by Headache.
I could understand public school supporters getting pretty steamed about this setup--I know there's not a lot of support for vouchers among public school teachers. I don't really feel a need to defend the policy (or to apologize for it). It just is what it is. I'm here to educate the kids put in front of me. I don't worry about much beyond that.