Yes, I paid the full second year.
Heres how I ended up breaking down the situation:
Case 1: I signed a contract and I should abide by it, word for word.
Case 2: The contract has a specific intent and purpose that doesn't necessarily apply to my individual circumstance, so maybe there is some way around it.
In the end, I decided that it was not worth fighting. There are a lot of people out there way worse off than I am and no one is taking away money that I don't already have in my bank (the repayment was deducted from the payout of unused vacation). In the end, I think that what constitues "fair" would be for me to pay the prorated amount for time not served. Though I ended up paying for the full year, I'll get by.