I went to a small liberal arts school for an undergrad degree in STEM, and to a R1 research university for graduate work.
The absolute best classes at the big-name research university were about as good as the average class at my small undergrad. The classes at the small school were of distinctly better quality: more engaged teachers, more engaging work, and simply higher quality teaching.
Most undergraduates don't realize it, but the purpose of going to an R1 is access to an alumni network and (for the small percentage that are interested) access to people performing cutting edge research in a discipline and their physical resources.
I suspect that honesty in their marketing materials would not increase applications though.