I used to work for a public school system that had a very similar training repayment program. I was required to take X amount of training hours, and could elect to pay for them myself or have the district pay. If I paid, then I could quit at any time with no financial repercussions (aside from loss of a job...) but if if the district paid, I had to agree to work for them for at least 3 years. If I quit any time before the 3 years were up, I had to pay 100% of the training costs.
The really messed up part was that they claimed that people would be responsible for their previous training costs even if the district fired them within that 3 year window. It turned out that they tried it a few times, and ended up getting smacked down in court every time. The clause was still in the contract, but by the time I worked for them, they never attempted to enforce it any more.