It’s clear the OP went into this whole process saying (thinking??) that money was not an issue, and the the kid applied to schools accordingly. Unless either the family’s financial situation has substantially changed or the parents had grossly miscalculated their ability to pay, it’s more than a tad disingenuous at best – and cruel at worst – to now say that money is indeed an issue, or that you are no longer willing to pay for Princeton, or that you will only pay as much as the cost of a UC.
That said, it is certainly within your right to pay as much or as little as you see fit, given that it is your money. Actions, however, have consequences, and if your son thinks that you are begrudging him something that you promised him and that you can indeed afford, he may end up being resentful. I clearly remember my father wincing and making some rather distasteful comments as he was handing over the registration check after I had decided to transfer from a very affordable state school to a private university (something my parents could certainly afford to pay for – the truth is, my father simply did not want to fork over the $$). I should point out that this was nearly forty years ago. I also clearly remember, nearly two decades later, my mother encouraging me to go back to graduate school and offering to help out with finances – no strings attached. Three guesses which of my parents I remember more fondly with respect to this (and most other things, but that’s fodder for another discussion). Apparently I am not alone in carrying resentment cross the decades, as @3girls3cats can attest.
The schools that the OP was looking at were not ones that give merit aid. If the parents knew they would not qualify for financial aid, they should have encouraged their son to look at schools that would give merit. If he has the stats to get into Princeton, I’m sure he could have gotten some generous merit elsewhere. Obviously, at this point, merit is off the table, but he does have some mighty fine options. Berkeley is a great school and, unless money were truly no object, it would be hard to justify passing up Berkeley’s EECS or UCSD’s CS or UCLA to pay full freight for a private university. (Mind you, schools like Princeton, Harvard, Yale or Stanford make it harder still). If Berkeley (or another UC) does not have programs that your son is interested in or if they are truly a terrible fit, that’s a different story.
We are trying to be as transparent with our daughter as possible. She understands that we have an exhaustible supply of funding that can be used to help pay for a variety of things, including her undergraduate and graduate studies, travel and study abroad, and possibly helping her with a down payment on a house or apartment someday, and funding our retirement. She knows that if we have to pay full freight for an undergraduate education, there won’t be as much left over for grad school and everything else coming down the pike, and that we, as a family, will continue to make financial decisions based on numerous factors.
For this reason, we are encouraging our daughter, a junior in high school, to cast a wide net that will include one (or possibly more) reachy-reaches of the HYPS variety; a few equally reachy-reach full tuition or – better still, full ride scholarships – at several high-ranking private research unis and LACs (again, provided they have programs that are of interest to her, and provided they are good fits); several in-state publics (again, provided they have programs that are of interest to her, and provided they are good fits. We, too, are lucky that we live in CA and have some great public options); and a few safeties (both from a financial as well as from an admissions perspective).
We don’t anticipate that we will be getting any FA – we qualify from an income standpoint, but we have enough assets to not qualify for need-based aid (a good problem to have, I suppose). So we are doing our research and maximizing our options. When the offers roll in (and we hope there will be some good ones), we will figure out what makes the most sense. Does an HYPS at full pay make sense if there’s a full ride or full tuition someplace else she wants to go? Probably not. Does HYPS make sense if her best offer is a $10k merit from someplace she’s less excited about? Absolutely. Time will tell.