Thanks guys. That's kinda what I was figuring. I forgot to mention that the left seat pilot is an MEI. So he could be providing dual toward the high alt endorsement per 61.31(g)(2). Does that change anything? Also, I was thinking considering what we've discussed so far means commercial students can't log PIC in a complex airplane either. Another similar interesting thread here:
Logging PIC during complex training - Jetcareers