A UK issued licence is essential if you want to fly a G-reg aircraft outside the UK. But you can - and many people have: so long as it's all ICAO compliant you need no special permissions, just customs/immigration and flight plans.
A US issued licence is essential if you want to fly an N-reg aircraft, then again you can fly that around the world if you want.
But my Canadian validation allows me to rent and fly a C-reg aircraft when I take a few days off whilst on business in Canada. I'm not going to take a fortnight to fly my AA5 over Greenland - I'm going to fly Air Canada, but grab the opportunities to fly a bit whilst there.
Learning and correctly using local RT is the captain's responsibility. It's not that hard, but before renting outside my home patch, I'm always careful to get a thorough local briefing. On long international trips, particularly VFR, then it's more difficult but there are documents available - or just explain in clear (aeronautical) English your intentions and generally it's not that problematic.
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