I'm with SMOE, and I've never heard of this, but I've only been in a semester.
I had to fill out a signin sheet during desk warming, and I noticed that the teacher before me had a fair amount of entries that said "Co-teaching training" and other things. I don't remember if one was specifically cultural.
I haven't had any days like that and haven't had to fill out a time sheet except for sick days.
A couple of times last semester, all teachers did get time out of school for a cultural experience, but my head co-teacher let me go, because they were doing things like watching a Korean movie. I didn't have to write anything, though.