Per the "admissions" part...to me it is NOT in any way tied to the recent Hollywood buy in scandal. The way it's been for awhile is the various athletic coaches basically get a certain # of spots. Ex: Crew = 5, Soccer = 7 FB = 15 BB = 3-4 (and similar allotment for women's teams.) Then the coaches do their recruiting (and students/coaches/families also reach out to pitch themselves too.) The coaches usually "rank" their kids they are interested in (but are often competing against other similar schools for) and then can tell the admissions office here are the ones I'd like. Most all of those kids have "pretty good" grades, but very possibly wouldn't get in on grades/essay alone, but rather the "sports" gets them the extra nod in. I don't think that's "cheating" in any way, their talent in sports got them a notch up and into the school, but they still have to be good students at this level.
As per the $/tuition piece, I'm not 100% sure of granular details. I do know that many of the athletes do qualify for financial need packages that can be a "de facto" scholarship. But that can be anyone too. Ex: If accepted to Princeton and believe if family income is under $100K (maybe $80K) tuition is free for any student. Clearly there are some kids from wealthy families whose kids are good enough to do say soccer/crew, who may not get any financial aid, but the families are able to pay the tuition and the sports simply helped get them in. But it's a legit player/athlete on the team, not the "fake photos in a crew boat" like the USC scandal.
Yes the Ivy's have started to send a few guys to the NFL and there have been a few who've had a shot at NBA, but by and large, the Ivy sports are almost more like D-2 level. The Duke, Stanford, Northwestern & Vanderbilt's are all so popular that they've become almost as hard as the Ivy's to get into now, but those are still real D-1 level programs as evidence of course by Duke in BB and Stanford in FB. I'd probably throw Notre Dame in the second group of prestigious schools hard to get into with top level D-1 athletic programs too.
The B10 has great schools that are becoming more and more popular with East/West coast kids, and the schools love the out of state tuition they get from those families too! I don't think anyone should hold their nose up at a B10 or ACC school and the education one can get if they really apply themselves and seek out all the opportunities one can find there. But if you are being truly honest about "market perception" think it's fair to acknowledge that to many the Ivy's are still the tops, the next tier (Stanford/Duke, etc) is pretty high up and then there are some state schools perceived a bit higher than others in the B10/ACC. Would say Michigan, UVA, North Carolina are examples of those. But then from there, most of the remaining schools are all considered really good with great campuses, student life, niche programs of expertise (i.e. Kelly, Purdue Engineering) etc.
Lastly, given how important grad school degrees have become, if someone were taking the long view they'd say "take the full ride at a great B10 school, do well and then have a great shot to get into a good grad school (who don't just want a class full of Ivy League undergrads!) and money saved from college scholly to put towards a future graduate degree program.