Also, regarding the time on the ground in MEM during day or night hub turns. You’re not “on duty” by any stretch of the imagination. You’re in domicile, your trip is over, you’re off the pay clock and not accruing any per diem. What I think he meant to convey is the time you spend turning in MEM counts toward you total duty because it’s not long enough to constitute a legal rest period.
My theory on the “rhyme or reason” of weekend layovers versus deadheads is simple dollars and cents. If it’s cheaper to deadhead a crew out on Fri/Sat and deadhead another in Mon rather that pay two pilots for the layover plus per diem, then the bean counters make the call.