Um, no. No such rule about O-7+ not being able to fly solo. Happens all the time, especially when it comes to F-teeners flexing about whatever new shiny toy the MIC got them this year for Xmas.
When it comes to seeing eye dogs in multi-person aircraft, in the USAF there is no rank in the cockpit. We go by seat qual, not rank. Yes, in practice humans are petty and everything is political, but by the book there's no rank in the cockpit. I've been the Aircraft Commander of a nuclear PL1 asset internationally, where I was the lowest rank holding member of the entire crew.
I've also been the A-code (mil equivalent to FAR 1 definition of PIC) as an O-4 with an O-8 sitting in my other pit. He was rightly told to sit on his hands and not touch anything yellow-jacket colored. I did add "please sir, thank you", of course. I am an officer, and by definition a gentleman after all.
The reality is that most of them appreciate the camaraderie of olden days, things that today are relegated to our closed door "meetings", since speaking loudly and frankly at the squadron bar (not even allowed to be called that, we have to call it heritage rooms now) is generally eschewed these days. So being told by a 3,300+ hour UV-faded patches wearing Iron Major (
<--) that your 3K setup was a graping mess, is viewed relatively fondly by those who wish to retain credibility with their flying and fighting subordinates. It's the discredited boot-licker careerists that usually try to pull rank in the cockpit or the squadron bar. But credibility is something you can't feign your way around in a room full of type A-(hole)s.
ETA: As to the distinction of aircraft commander vs mission commander. Yes that does exist in certain contexts, but in the instance where the mission commander is on board an aircraft where the aircraft commander is of lower rank, again the A-code still retains ultimate safety of flight authority over the ownship. Again, rank is immaterial.