Valid in this context means not suspended or revoked. This has been covered on here many times. A european pilot licence cannot be used in europe without a european medical, but it doesnt mean its invalid if the medical is expired. A FAA medical can be used.with a 61.75 cert and the currency requirements are simply BFR/FAA currency requirements not anything else. The underlying licence needs to be valid, as in not revoked, and the underlying medical certificate can be expired provided an FAA medical is held. OR no faa med and a valid underlying one.
The only exception to this is when operating outside the USA. Many countries ( UK,EASA member countries) require residents to hold a local certificate that is both valid and usable to fly in that country. (note - country. EASA is not a country)
In the UK , where I am resident, I need a UK cert / med to fly my N reg, but as soon as I leave UK and enter france I have to have a FAA cert and medical. A french person needs a french issued easa cert until they fly to uk or germany in an N reg.
And whilst on the topic, paper 61.75 haven't been valid for a very long time yet I still see people trying to use them. And the foreign licence number must be an exact match for the number on the 61.75. If you go from say, ppl to cpl, the prefix changes and you will need a reissue.