Each time, someone is able to point out a problem isomorphic to the one given, but lacking a characteristically anthropic component to the reasoning.
To me, that just indicates that anthropic reasoning is valid, or at least that what we're calling anthropic reasoning is valid.
Well, that just means that you're doing ordinary reasoning, of which anthropic reasoning is a subset. It does not follow that this (and topics like it) is anthropic reasoning. And no, you don't get to define words however you like: the term "anthropic reasoning" is supposed to carve out a natural category in conceptspace, yet when you use it to mean "any reasoning from arbitrary premises", you're making the term less helpful.
One day, you and the presumptuous philosopher are walking along, arguing about the size of the universe, when suddenly Omega jumps out from behind a bush and knocks you both out with a crowbar. While you're unconscious, she builds two hotels, one with a million rooms, and one with just one room. Then she makes a million copies of both of you, sticks them all in rooms, and destroys the originals.
You wake up in a hotel room, in bed with the presumptuous philosopher, with a note on the table from Omega, explaining what she's done.
"Which hotel are we in, I wonder?" you ask.
"The big one, obviously" says the presumptuous philosopher. "Because of anthropic reasoning and all that. Million to one odds."
"Rubbish!" you scream. "Rubbish and poppycock! We're just as likely to be in any hotel omega builds, regardless of the number of observers in that hotel."
"Unless there are no observers, I assume you mean" says the presumptuous philosopher.
"Right, that's a special case where the number of observers in the hotel matters. But except for that it's totally irrelevant!"
"In that case," says the presumptuous philosopher, "I'll make a deal with you. We'll go outside and check, and if we're at the small hotel I'll give you ten bucks. If we're at the big hotel, I'll just smile smugly."
"Hah!" you say. "You just lost an expected five bucks, sucker!"
You run out of the room to find yourself in a huge, ten thousand story attrium, filled with throngs of yourselves and smug looking presumptuous philosophers.