If the first statement were true, it would be legal to trigger an in-game macro with third-party software if the macro is bound in-game to F1, but it would be illegal to trigger the same macro in the same way if it's bound to Alt F1.

I think the second statement is the correct one. The second statement says that the client's key bind screen is the rule book. If it's legal to bind a certain in-game action to a certain physical key combination with the client itself, then it's legal to do the same thing with third-party software.