It becomes my job when someone asks... until that moment, I have no responsibility for their outcome.

No, it becomes your job when you choose to make it so.

(nods) when my carefully-considered, rationed request is blithely blown off by the other person as being of no consequence, yes, that gets to be annoying...

You know, what I'm getting out of this discussion is that when you make a request of me, I'm unable to say no without it being a Big Deal[tm] for you. Am I wrong in this?