I think the rules are quite clear, but we've been spoiled because they haven't been enforced. Now enough people are taking advantage of the fare variations that it's gotten a little notice at BA revenue management.

The point of all those fares is clear: to buy a ticket at the Turkish price, you're supposed to be sitting in your apartment in Istanbul, with a wallet full of Turkish currency (there is/was a currency-of-payment rule). The fact that BA choses to pick up your call in Bremen or Mexico City is their business. After the call and the arrangements, a BA agent or proxy (at IST these days) will run your Turkish credit card and hand you your tickets.

Anything more generous than that is a gift from OW. Right, OWE wizards?

The OP's next step is to cancel the res made so conveniently with BA/Canada and try booking it directly through the IST/Bremen line. I can't guess if he has to hoodwink them by not giving them an excuse to know he's communicating from the US, or if he can be up front about it. A cautious approach might be to have an unrelated friend call Bremen and ask if they'll take an itin and price it ex-IST, and accept payment with a U.S. credit card.

If BA and the others go forward with playing by their rules, then as I said the search is on for qualified TA's in cheap cities. The agent is of course "your agent", acting for you as if you were standing in his office, afaik. Not that I'm having any luck getting hold of one in Damascus, of course.