The sample size of our records is incredibly small when stacked against the history of the earth and all the records we're missing.
"How unlucky we would have been to see this data of the past, if a spike in temperatures had actually happened then" is P(data|hypothesis), the frequentist argument for or against a hypothesis. It's what a p-value is, but arguing what to call it is pointless anyway.
At the same time I wouldn't be surprised if there were climate scientists who chose to avoid these sorts of calculations.
Also, the p-value might tell you whether or not an event like this would literally be one of your samples, but its not whats going to tell you whether or not a reconstruction from these samples contains information about these events. Although I guess its not much of a distinction.
Heres where we disagree.
If you're right and all of them have overlooked it, you'll have material for a hell of a paper yourself: There's nothing more juicy than a paper that mathematically proves that a pile of accepted scientific literature is flawed.
Imagining possible flaws of a paper before reading it is so easy that it's hard to really strike gold (it is equally easy for the authors and reviewers). But it is also an enjoyable way to learn how those flaws have been taken care of.
And lets not pretend one or two papers that make bold claims hold much water.
I've been misled by popular media many times, so color me unsurprised that they might be selling some bullshit about this as well. (Not that they certainly are.)
The AGW papers I've read, though, are very solid, and more sophisticated than I expected.
NOAA researchers corrected for the "cold bias" from buoy measurements compared to measurements made in ship engine rooms.
My point isn't to deny the climate is changing but to call into question the quality of the data being used to create models and formulate policy. Each source of measurement has inherent bias and error -- that's the nature of scientific measurement -- especially measurements that often occur in the hulls of a ship. Who calibrates the measurement devices? Who calibrated them 50 years ago?
As in "I learned this model in a dark alley in Stalingrad, and I won't defend it in my paper"? Good luck trying to publish a paper if your model isn't well known and you don't explain it.