Not sure about an admission preference, but certainly free tuition is a fairly common benefit at many higher ed institutions (it has been offered at both privates that I’ve worked at). IIRC, when I applied for a job at MIT years ago, the benefit was 50% tuition assistance wherever your child attended (given that admission to MIT was highly unlikely for most).
Also, re: tuition exchange…definitely not a guaranteed benefit for anyone, even if your host school (employer) guarantees your kid an exporting slot (my school holds a lottery for 5 slots each year). The importing school has to award it, and it really is just like a merit scholarship with a smaller group of applicants.