In the plain language of the regulations.
The definition of "operate" in 1.1 is not that narrow.
"Operate, with respect to aircraft, means use, cause to use or authorize to use aircraft, for the purpose (except as provided in §91.13 of this chapter) of air navigation including the piloting of aircraft, with or without the right of legal control (as owner, lessee, or otherwise)."
If there were no certificated pilot on board, would you claim that
no one was operating the aircraft, for the purposes of 91.109(c)?
Yes, as Kramer would say that plane was "outta control!" Who is using the aircraft or authorizing it? Assuming it's not a joyride or stolen - the pilot is authorizing the operation. The non-pilot is a carbon based autopilot, the pilot is the operator.
91.109(c) doesn't say anything about backing anyone up. That concept is your own invention.
Really, so you can be the only person in the plane, and be a safety pilot? Look at all the other common uses of safety. Safety line, safety cutoff, etc...all operate as a backup, not as a primary. As the only pilot, you aren't a safety pilot. Ergo 91.109 isn't applicable.
What makes you think that a non-pilot can't log the time? 61.51(g) uses the word "person," not "pilot."
What would the non-pilot (legally) log it as? Non-pilot, no instruction given, there is nothing to log.
The regulations don't say that no instruction is being given; they only place restrictions of what can be
logged as instruction.
I was drawing a parallel.
If the logged instruction isn't legal/doesn't exist happens, because there is no CFI, the safety pilot doesn't exist, because there is no pilot to be a safety pilot to.
What regulation prohibits the non-pilot from logging the hood time?
See my previous comment as what he would log it as.
I'm happy to defer to the plain language of the regulations. Your options are to do the same, or try to get the Chief Counsel to agree with you!
I assert your interpretations are incorrect.