I'd be surprised if this ever saves anyone much money, and I think it will usually cost you a lot. My guess is that the merchant (or its bank) is building in about a 3% fee in their conversion to dollars. Since most credit cards now charge a fee for either a charge in foreign currency or a charge in a foreign country even if in dollars, you'll get your card's fee added on top of the merchant's fee. Most US cards are now charging a 3% fee so this gimmick will likely cost you another 3% on top of that. Some convenience.

Has anyone encountered a situation where the overseas charge was run through in dollars without asking or when you asked to have it in the foreign currency and they did it in dollars anyway?