Obviously, I was only talking about public schools with the player only getting a partial scholarship. Private schools are typically the same cost regardless whether you are in state or not.
For example, these numbers taken from the collegeboard website.
University of Illinois
In State Tuition - $12,524
Out of State Tuition - $26,666
Room and Board - $9284
If an out of state player gets a 40% scholarship for tuition and room and board, it would be approximately the same as an in state student without a scholarship.
Of course the numbers will vary depending on the amount of the scholarship, but as you can see the out of state tuition negates a significant portion for public schools.