Dude, doing something on an off day firstly doesn't make it an off day. An off day is a day you take off. Period.
However, our discussion in that thread was about doing abs prior to training on the same day.
If doing the abs on the "off" days are not harming you, then go along with it. Nothing needs to be set in stone. You're doing the right thing in your approach. If you see your lifts suffering, just take a day off in the true sense of the world