Tell me where I go wrong.
PP, drivers license medical.
I can fly solo in an LSA.
I can carry passengers and act as PIC in an LSA.
I can let some other person (pilot or not) manipulate the controls in an' LSA while I act as PIC.
Good so far.
I can let some other person (pilot or not) wear a hood while manipulating the controls while I act as PIC in an LSA.
Stop. Now you're acting as a safety pilot. 91.109 says "No person...," not "no pilot." Therefore, regardless of qualifications of the
person manipulating the controls, if that
person is using a vision restricting device, a safety pilot with at least Private is required, and based on that, 61.23 requires the safety pilot to have a medical.
I can not be a "safety pilot" so said other person can not log the time as simulated instrument while manipulating the controls with a hood on.
Since you cannot legally act as the regulatorily-required safety pilot, the flight is being conducted illegally regardless of what the other person logs. However, if that person is rated in the aircraft, and wishes to create legal evidence of that illegal operation, that person can log it as PIC and instrument time with your name as safety pilot, in which case you
both can be written up on the strength of that evidence.
If the other person is able to act as PIC of an LSA, I can put a hood on.
Sure, you can put the hood on, but you cannot legally manipulate the controls with that other person acting as safety pilot unless that other person is legal to do so, i.e., has a PP or better and valid medical.
If the other person has a PP and a valid medical I can log the time as simulated instrument, otherwise not.
If you're rated (or in the case of an LSA, have privileges) in the plane, you can log it regardless of the other person's qualifications. However, if that other person isn't qualified to be a safety pilot, your log entry is creating evidence of violations of at least three regulations by the both of you.
FARs are written in blood.
That's generally accepted to be so, but sometimes they are written by people simply trying to close loopholes. And remember that there is no regulation prohibiting the manufacture of rope which the FAA can later use to hang you. If you want to put flights which violate various other regs in your logbook, but what you log it IAW 61.51, you are not in violation of 61.51, even though you are creating legally sufficient evidence of your other violations.