Mom and I quickly made friends with a driver in JA. He took us all over, and one day he pointed out a big sexy house the zepplinites had rented for a holiday.
I spent a lot of time in Jamaica during the 90s, but the crime there is currently widespread - rather than pretty much limited to Kingston, Spanish Town, and environs as it was back then - and the amount is frightening.
IIRC the British government fines airlines if passengers don’t have passports and visas (if required), so the airlines do check everything.
There have been some cases where airlines prevented passengers boarding flights from the UK to the USA because ICE had already told the airline that those individuals would be refused entry.