Parents say they should have gotten my student tax credit

I was 19 and a full-time college student. I paid for 100% of college and life expenses. I worked part-time and made around $10,000 a year. I lived on my own. The only money I received from them was for my birthday or Christmas, but was never over $100.00. They tried to claim me as a dependent and claim my student tax credit. I filed as an independent and got the credit. My parents say it was their credit and I took it away from them. Did I file correctly? *note* I took out student loans in my name to pay for tuition and books. Nothing was payed for by anyone else. I was a waitress and one year I made 12,000 one year I made $9,000.