This isn't entirely true, due to various entangled trade agreements that require countries to respect each other's intellectual property as a prerequisite.
They require countries to respect each other's copyrights, not each other's copyright law. The US, for example, does not enforce EU database rights. Moreover, you can in EU copy a book made by a US author who died 80 years ago even if that copyright is still valid in the US. Local laws are enforced by local courts.
What the Berne Convention requires is that if I have a copyright in US it will be recognised in France, etc without having to re-register it in every country in the world.
There is no part of the Berne convention that will prevent people from training models on US copyrighted works outside of the US. That is entirely a matter for local jurisdiction.
This isn't entirely true, due to various entangled trade agreements that require countries to respect each other's intellectual property as a prerequisite.
See https://en.m.wikipedia.org/wiki/Berne_Convention