Don't have any problem with any of that.
You certainly need an "appropriate person" to conduct a BFR/AFR/HFR. But, I am an appropriate person within the meaning of the Regs, so is there any prohibition on me (as a 'appropriate person') reviewing myself (as a licensed pilot) ?
Analogous situation not so long ago when I had to write a letter from myself (as the managing director), to myself (as an employee), with instructions that limited the use of a company vehicle. One person, two different hats. The action was required and endorsed by the Australian Tax Office.
I know what should happen, it's obvious. But obvious isn't always right, and I still think it's a fun question.