I used to call it in, or fill out a form online for my travels. I've stopped several years ago, and have never had a problem when using cards at a physical POS in all of the foreign countries I've visited.

I've had airline charges rejected when purchasing online, but that only happens when I'm purchasing outside of my normal purchasing pattern. I normally buy tickets when in India for travel to Thailand. Once I've relocated to Thailand, first time purchasing a ticket in Thailand for travel to India got denied. Called it in, and it cleared, and ever since, never had another problem with that.

Surprisingly, with a credit card billing address in California, US, the company actually detected an actual fraudulent charge in a city near my billing address. And the charge was for less than $10!