I am afraid very little is ever "achieved" on this front. These issues just go round and round.
I am sure some aviation lawyers have formed a view on it but they sure as hell are not posting it on here.
Until something gets clarified, my view is that the applicability of regs like 61.3 to scenarios outside the USA has to be read
literally as it is written.
So, for an N-reg, you need a license
issued by the owner of each airspace in which you fly, unless you have an FAA license in which case you can go anywhere.
On a slight digression, I have done an awful lot of digging and there really isn't much point in being on the N-reg unless one is using the FAA IR. Maintenance wise, the only significant advantage is the absence of the UK 150hr check but that doesn't affect many private owners! The other big advantage is a better system for modifications but again not many people do that many mods. There are some medical concessions but they go away if you can "somehow" get through the JAA Initial medical because you are allowed Demonstrated Ability after that. EASA is highly likely to do away with this Initial/Renewal difference anyway, since it serves no aviation safety purpose.
A state has jurisdiction over its own airspace
Of course, but this normally works in the "prohibition" direction (the example you gave) and would not normally
permissively override a restriction imposed by the state of registry. I suppose it's possible (and I know others have argued so) but I have never ever seen the slightest example of such a situation.