Income plays a role in determining eligibility. So it isn't just about having money in the bank.
I have a decent amount of money in my 401(k) - but I'm not sure I'd take it out to pay for a car or a kids schooling.
But I had a similar experience of a bunch of things all hitting us at once and killing my savings for a bit - which made it so I would have a hard time helping a kid pay for a semester of school.
Car died - so new car with a new car payment, wife had to have an MRI and then surgery on her foot (combined with a high deductible health plan), and then another son had some travel issues that we ended up helping pay for a pair of airline tickets unexpectedly. Just like that - not much left in the bank. But give me some time and I can start building it up again.