Checking that box does not give them authorization to deduct anything from your bank account; it gives them authorization to deduct it from future deposits they are making into your account.

If you had checked no, and they had given you funds that you were not entitled to, they would issue you a bill payable in full immediately. This would come from court and be a court order for you to repay it in full and if you don't, they will garnish your wages.

You did the correct thing imo.