Yes this is controversial.
The game designer thinks one thing and the North American hobby thinks another.
Anyway it looks like Kestas agrees with the North American hobby, that coast is not significant in the support order, so that if it is specified differently in the move order and support orders, that difference is ignored. So pity poor Russia that orders Rum S Turkish F Con-Bul(sc), and the Turk orders F Con-Bul(ec). The support is valid according to the hobby, but not to the game designer.
Allan Calhamer says "Allies should be in evident agreement", or to expand his extremely terse English, "Allies should be in agreement, and there should be evidence that they are in agreement".
To me the game designer's reasoning on this subject is sound, and if we've been playing it wrong all these years, so be it.
What follows S in the written support order looks like a move order for the supported unit. It has the same syntax. For the support order to be valid it makes sense to require its last section to be a valid move order. In other words if it looks like a duck, it should quack like a duck.
I suspect that this was so obvious to Allan Calhamer, that he didn't bother spelling it out in the rules.