I hope I can explain this clearly. They are correct. If you look back at the end of your 15:38 of duty, you only find 8:22 of rest in the last 24 hours. Therefore, you were previously reduced even though you were off the previous day. (I know, doesn't make much sense) So after you have a reduced rest, you need to have compensatory rest to be legal.

Hope that helps.
jrmyl