If you CHOOSE to turn down a “top” school, it should be because you really believe your choice is best and will never regret it. That is possible and good. (If the financial aid package could not be negotiated to something you can manage, then there is not really a choice. You go where you can.)
But too many people who make that type of choice when it is a real choice (i.e., when their family CAN afford it), regret that choice.
I grew up with the story of how my dad was admitted to Dartmouth but his mean father (who was also abusive and broke his nose twice and knocked him unconscious sometimes) told him, “I can pay for Dartmouth if you want to be a parasite and live off the fat of the lamb. Or you can be a real man and work and pay your own way through a school you can afford.” My dad got angry at that statement and made the decision to work his way through CUNY Brooklyn. He always regretted it and never stopped repeating that story.
My son’s English teacher in high school told him how he had been admitted to American, but went to a state university and always regretted not choosing American.
A colleague of mine told me he had turned down Notre Dame for the local state university and has always regretted it.
During my son’s application process, we kept hearing stories like that. So when, at some point in the process, my very considerate son realized how crazily expensive private colleges are and mentioned, “Maybe I should save us money by going to Binghamton,” we thought it worth saying what we did. We told him that Bing is a great college, and we will be pleased and proud if he chooses it. But if he chooses it, it should be because he thinks it is the best fit for him, not because of money. We told him we have saved and made financial choices his whole life to be able to tell him he can go wherever he wants. Go for fit, and do not worry about money.
So, my thought for applicants: go where you can afford. But if you get a good aid package, OR can afford full tuition, at the “best” school (to use the OP’s language), then if you choose a less “prestigious” college, you had better be prepared to state proudly your whole life that that is where you went, and that it was a great experience. But if, for the rest of your life, you are going to preface every conversation about college with, “I COULD have gone to [other college],” then if you have a choice, choose the one that does not require an explanation!