Yes, because you are claiming yourself for 2020 and the stimulus checks were advance payments to folks to get them through 2020 (or to help, of course). The claiming of yourself for 2020 (in 2021) is with respect to prior year - as was your parents claiming you for 2019 in 2020 and prior - it was in the year that just passed by. The stimulus payments that went out were for current year. I hope that makes better sense! The money is yours as the IRS back in the Spring of 2020 was going by 2019 filed tax returns, that's all.
