Widely used US general liability wording defines a coverage territory that includes the United States, its territories and possessions, Puerto Rico, and Canada. It then extends that territory to all other parts of the world for injury or damage arising out of goods or products made or sold within the primary territory.
That extension is real, and it is why a broker can accurately tell a device manufacturer that products coverage is worldwide. The part that gets summarised away is the condition attached to it: that the insured’s responsibility to pay damages is determined in a suit brought within the primary territory, or in a settlement the insurer agrees to.
So a claim from a device sold into Europe may well be covered, provided it is litigated in the United States. A judgment handed down by a court in Munich, Tokyo, or São Paulo is a different question, and it is the one that has to be answered before a distribution agreement is signed rather than after.
Check the same definition on the umbrella and excess layers. A broadened territory on the primary achieves little if the layers above follow narrower wording, and following-form language does not reliably carry a manuscript endorsement upward.