Thank you all for your responses.

A couple of comments. Warsaw Will says that the insistence on "me" seems relatively recent. The article in the NYT says that the insistence seemed to come about in the 19th Century which is a long time ago. The other smug article which you cite is angry and aggressive but is it not correct? To quote from the smug article: "This particular mistake seems to be made most often by people trying to sound smarter than they are" which is precisely my point. This is somehow different from the majority of grammatical errors. This is perpetuated by (I can't think of a better way to put this) those who should know better.

JJMBallantyne you are absolutely spot on (as others are) when you state that teachers hammered away at "I vs me" ad nauseum, resulting in the hypercorrection that we now witness. I would argue however that it is not now accepted usage. Using "me" as the subject in a colloquial sense is more an accepted usage.

I sincerely hope one day that I will be less phased by this phrase. To be clear, I'm not a grammar fascist. I understand that grammar evolves and mistakes become accepted. Perhaps it's the faux-pomposity of this mistake which makes it stand out...