When you set out to correct a person, make sure you know what you are talking about.
I am well aware of the expression, which just happens to be "hoist WITH his own petard" not "Hoist BY his own petard", I just happened to mistype hoist in my haste to put something down quickly. While I know a bit about words, I am the world's worst speller.
Since it was in the past, it would be hoisted not hoist. Since it was a newspaper, not a person hoisted by its own petard, its was more appropriate than his, IMHO.
I know exactly what a petard is, having looked it up years ago.
"For 'tis the sport to have the enginer / Hoist with his owne petar" -- Shakespeare, Hamlet III iv.
"Hoist" was in Shakespeare's time the past participles of a verb "to hoise", which meant what "to hoist" does now: to lift. A petard (etymology: to fart) was an explosive charge detonated by a slowly burning fuse. If the petard went off prematurely, then the sapper (military engineer; Shakespeare's "enginer") who planted it would be hurled into the air by the explosion. (Compare "up" in "to blow up".) A modern rendition might be: "It's fun to see the engineer blown up with his own bomb."
Of course there are lots of variations on the hoist/petard theme, e.g., this headline and summary in Capitalism Magazine found at http://capmag.com/article.asp?ID=839
Hoisted by Their Own Petard and this summary of the same article,
Summary: It is Mr. Gore who was hoisted on his own petard. He who seeks unconstitutional, standardless recounts and tries to delay federal challenges to them, is in no position to complain that time has run out when the federal courts finally rule.
So it is wrong to claim that the phrase is "Hoist by his own petard", since that is neither the original quote from Shakespeare nor the only acceptable version of the quote.
I thank you for your effort to correct what you took for my ignorance and I hope this helps.
In any case, I am delighted that the New York Times are hoist with their own petard, political correctness of the type they champion, for example by supporting Martha Burk in the Masters controversy, blowing up in their faces and surrounding them with a rank smell.