If their record keeping is anything like yours, I wouldnt say its safe to assume anything
While I know in my case that the "date of record" for tution is the date they actually bill me, and not the date I pay it, I can't say the same is true for you. I am not a tax law expert, I was just sharing one of my experiences in hopes that it might explain the discreptancy for you. Fortunately for me, my schools website specifically addresses this issue which is the only reason why I know.
Were you ALWAYS paid by check? Any payments in cash that you thought may have been "under the table", they may have decided to report anyway...