We told DD that we’d pay for undergrad (tuition, room/board, medical) and she was responsible for grad school if that was her choice. She applied to publics and privates and got into a mix of both, eventually selecting a top state school. She loves being debt free, as do we. We also only have one child and live well within our means because that is our comfort level with debt. My husband’s parents paid for his tuition, but mine was a combo of parents, loans, grants and work study.
I don’t know what kind of conversations DD has with her peers about college debt - most of her roommates have been fortunate enough to have parents pay the bills (and some pay for a lot more than we did). At the end of the day, there are people in your life that make/have more or less than you do - it’s an important skill to navigate that. You can do it without lying or bragging.