Well lemmie see-—if junior registers to vote in Frostbite Falls (home of Watsamatta U.). That means he has established a residence, and must NOT be a dependent of Mommy and Dad.
Ergo, they cannot claim junior as an exemption, and he no longer is eligible for their health insurance until he gets his PhD.
In a more perfect world, your scenario is probably correct.
In the real world, I’d guess the cross-reference never happens.