While that has become more true now, that wasn’t so true a decade and half ago or more.
When I was an undergrad and for a few years afterwards, the dynamic I observed and heard about from town locals who attended Oberlin or were HS students was the following:
Cream of the crop of the students from the Oberlin area tended to overwhelmingly choose East Coast elite/respectable universities/LACs. This was especially the case with faculty children. Schools they ended up attending were Harvard, Amherst, Dartmouth, Swat, etc. Only exception was aspiring engineering majors as they gravitated towards Ohio State*.
Those just below that cream of the crop attended Oberlin or peer private colleges.
With the exception of engineering, Ohio public colleges were regarded for anyone else who had viable college aspirations.
Incidentally, Midwest public colleges were also doing their utmost to recruit students from the coasts just as much as their private LAC counterparts when I was a HS student/undergrad. One illustration of this was the exceedingly lowish stats required for classmates from mine and overlapping graduating classes needed to be admitted to ones which were elite in their own rights such as UWisc-Madison**.
- One of my engineering uncles is an alum.
** Knew several HS classmates who were admitted and attended UWisc-Madison with HS GPAs as low as C/C-…but highish SATs.