Can my parents claim me as a dependent?

I turned 24 in May of last year. I was a full-time student in a different state until October. In July, I started working full-time, in a different state. I don't live with my parents, and I pay my own rent. My parents claimed me as a dependent on their taxes this year, because their tax person at H&R Block told them they could. But I looked online at the IRS' website, and it said the child had to be under 24 at the end of the calendar year. Am I missing something and they're right? Or did she file their taxes incorrectly? 

I have to do my taxes soon, and I just want to know what I need to put down.