I agree - k-12 achievement should be related to k-12 spending, not college tuition.
Reputable economic research into college economic productivity looks at budget per full-time student measures rather than tuition price tags. The amount actually spent varies from the sticker price due to financial aid and endowments and so on.
Turns out that American colleges are a lot like the rest of our society. We lavish resources on a few elite schools, and there are a great number of lesser schools with a much lower level of resources. Surprisingly, the schools are equivalently productive for their level of economic resources available.
http://users.nber.org/feldstein_lecture_2016/feldsteinlecture_2016.html
I assume our spending on K-12 education is similarly skewed with some lucky few students getting much more than others, though I have no source to cite for that.