Either they'll flood it with honest requests, or they'll flood it to prevent honest updates.
I'll let Satoshi know about PoW. He'll be disappointed, but you're probably right
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You realize that a simple OTS gives you Bitcoins PoW practically for free?
And denial of service on a calender server? Meh..it does not even do anything if you simply delay publishing your event until after the timestamp of that event has been mined; at which point you would have to conspire with the calender server.
And if there seriously would be a scenario where that would be a plausible risk because we are dealing with something that high profile, you could just timestamp things with your own bitcoin transaction, and that would still be cheaper (and way way way more definitive of a defensive measure) than going a PoW route.