Yeah, there is no way they should be allowed to bill the estate which they themselves are administrating.

In a normal country with a social welfare program, the guardian would have to bill the government — if the government doesn't agree to lay down money to say that this person needs protecting, nobody gets paid.

(In an honest no-government-programs libertarian paradise like the US sometimes pretends to aspire to be, the guardian would have to bill some kind of health insurer that covered this specific care: and again, the insurer would take on the task of scrutinizing the claim.)