The US DoC has as much say for ARIN as it does for the RIPE NCC.
The US DoC, through IANA functions, says, e.g., what IP Address blocks each can allocate. That seems to qualify as 'much say'
Didn't say how much say, just said that whatever say it had for ARIN it was the same as it had for the RIPE NCC.
You seem to be confusing delegation of authority with loss of authority. The DoC has contracted the IANA function to ICANN and doesn't involve itself much, and ultimately plans to get out altogether. However, the IANA operator (ICANN) then has 'much say'. But the DoC 'get out altogether' event hasn't happened yet. So you can't write out the DoC just yet.
Don't how you arrived at that conclusion based on a casual observation. Not writing them out, don't know how you got that.
The RIRs existed before ICANN. The relationship between the RIRs and ICANN is defined in the ASO MoU, an agreement between ICANN on the one hand and the NRO on behalf of the RIRs on the other. There is no mention in the ICANN bylaws of the RIRs.
The fallacy of this claim was already stated:
What is false about those statements? RIRs get their authority
and IP Address Allocations, etc from IANA. The fact that RIRs existed before ICANN is irrelevant, because IANA existed before the RIRs. And, as I noted, IANA functions are now contracted to ICANN. Technically, it is in fact the IANA (not ICANN) that has direct control over RIRs. But, as I pointed out, ICANN has full control over IANA functions by contract with the US Government. And, as I pointed out, the IETF is a technical consultant to ICANN. The MoUs are just that: Memoranda of Understanding. MoUs can be terminated, and don't supercede the contracts with the US Government.
Never intimated anything about authority lines or derivation of authority, just pointing out some of the factors in the relationship between ICANN and the RIRs. Ray