By regulation a 61.75 is not a standalone licence. It needs to be issued 'on the basis of' something. The underlying licence merely needs to exist, it does not need to be current. That's what the flight review is for.
This is suggesting that two different licences are held, one UK and the other FAA but they are not. For the UK licence to be 'valid' then all parts must be in place and up to date and certified for the flight to take place anywhere throughout the world; Subject to ICAO If the pilot wishes to fly a UK registered aircraft in the US then there is no additional licencing procedures. Each ICAO state may have additional requirements for flying
its own aircraft. Only the CAA can certify a UK licence and its privileges, the US cannot.. The US rule 61.75 is an
additional requirement. for the operation of its own aircraft.