Port State Control is done by the Port State, not the Flag State, thus any PSC on an American flag vessel is done by a foreign entity in a foreign port:
When USCG inspect a US flag vessel in a US port or anywhere, it is as the Flag State Authority.
Here is the definition of Flag State Control as issued by MPA Singapore:
And the difference of the two in terms of ILO’s MLC’06 , which USA is not a signatory to, but have to comply with when US ships visit foreign port:
Here is a list of the Classification Societies that is approved by USCG to perform inspections on their behalf and which inspections they are approved for: