Going through the process now. Best advice I can give is the following:
1) Save money , but funnel it to an account in your mom's name. Or another relative. College pour over every last corner of your financial situation. They all work differently but be prepared to feel violated by the questioning. "How much is tuition? " "Well that depends, how much are you worth?"
2) Have a very smart kid. It helps. Colleges in effect are in competition, and their numbers are a huge part of their sales pitch. Kid get into their reach, expect to pay near sticker if you do decently. But if your kid is smart and from a well regarded school, those numbers are gold, even to good schools. Go down a peg, and they usually throw a fair amount of money at you. 65K (pretty much the going rate as far as I can tell) goes to 20-30K in a hurry if they want the numbers. There is also a fair amount of courting "this is my number 1" etc.
3) The money is available and people are borrowing it like crazy, so acceptance rates this year were driven down. Also, HS's are inflating grades to get their kids in better schools. College are inflating their grades so their kids get better jobs. So the competition is pretty brutal. Mine ended up getting accepted into some very good places, but also rejected at a fair amount that on paper (if your school uses Naviance, you know what I mean) where she seemed to be lock. Got into Nova early and they threw her 25k without any negotiating (yes, you can negotiate). She's not going, but those type of offers are out there.
4) The whole thing is a racket. Sometimes it's like the scene in Good Will Hunting when Will sends Afleck into his job interview and he asked for payola. Example, mine was wait listed at one of her higher end places and I called to see what her chances are, and the guy basically asked if I was interested in making a donation. "You situation, heretofore, would be greatly improved...."
5) As mentioned, the financial vetting process is intrusive. Been in your house for a while and have some genuine equity in it? Well, that literally translate to cash to some schools. Have a rental property? Well, that rent is your tuition answer! What's in your bank account? What's in your kid's bank account. What's in their siblings bank accounts? What's in your business account? It's ALL held against you and what they call the EFC (expected family contribution ) Oh you saved in a 529? Great, that's ours. And you have a decent job? You both work? I'm afraid you're looking at the full monty sir. FAFSA forms, CSS profiles, W2, 1099's - get used it when the time comes.
6) Some schools are need blind and meet the needs of their students. It seems to correlate quite nicely with the size of their endowments, but not always. For instance, a school like U of Rochester has 2.1B laying around. It's a great school and they were very willing to have a back and forth. Other places were not. Basically, take it or leave it. Also, when your next one comes around, there are some schools where you EFC will not change, as long as both schools are need aware. So, if you are paying say 45 for one, and have another one on the way, many schools do not expect you to pay more than 45 total - and drop their number in half basically. You basically get a 2 for one, but make no mistake, this does not apply to all schools. For example Tufts will tel you the average student debt upon graduation is 18K. Seems reasonable, right? Well, Tufts is not need blind - and it's a small school with basically 1200 spots to fill - they have plenty of full payers to choose from, and they favor them over need based students.
7)There is really no set formula for this. Some schools will really work with you, some will not budge. At the end of the day, most of the decent schools are the sellers and their product is in high demand. If the school is smaller, they simply do not need to fill that many spots. Many will simply take the full payers, even if they have lesser grades, and be done with it. But some are genuinely interested in bringing in the smartest class possible and if they like the student and the student shows them a lot of love, they will work with you to some degree.
8) Vet your schools for their alumni network. Some are awesome at this, some do a really poor job and don't focus on it at all. The object of this whole thing is to get a job in a field that your kid finds interesting and has a path too success and self reliance, and some universities to a much better job at helping kids connect to that interest, and finding the right people already in it who can help. Ask this question on every tour. You'll know the good ones (and the lesser ones) when you hear it.
9) To some degree it's all mostly BS. If you are smart and willing to work, you can go to Umass or Tufts and you'd probably wind up in the same place 5 years after graduation. The better schools can be a nice head start, and nice pin to carry around as you move ahead, but I'm not sure it really matters. I've meet my fair share of complete idiots at Yale, and have seen a few brilliant people that went St Nowhere U.
10) In the end your original point is valid. Not having money does in fact get you some leeway on the EFC, but make no mistake, the reason you got that leeway is because you don't have money and the leeway they give won't make it painless. They don't go from 65K to 15K - More likely they drop it to 40-45K. (which, you know, does say you 100K give or take over 4 years.) Throw in multiple kids and those numbers add up. Save and hide. That's my advice.