Yet another account, from the 1938 book Jungle Patrol, attributes the deed to someone other than Pershing:

It was Colonel Alexander Rodgers of the 6th Cavalry who accomplished by taking advantage of religious prejudice what the bayonets and Krags had been unable to accomplish.

Rodgers inaugurated a system of burying all dead juramentados in a common grave with the carcasses of slaughtered pigs.

The Mohammedan religion forbids contact with pork; and this relatively simple device resulted in the withdrawal of juramentados to sections not containing a Rodgers.

Other officers took up the principle, adding new refinements to make it additionally unattractive to the Moros.

In some sections the Moro juramentado was beheaded after death and the head sewn inside the carcass of a pig.

And so the rite of running juramentado, at least semi-religious in character, ceased to be in Sulu.

The last cases of this religious mania occurred in the early decades of the century.

The juramentados were replaced by the amucks ... who were simply homicidal maniacs with no religious significance attaching to their acts.

We haven't eliminated the possibility that Pershing at some point chose to deal with a group of "Mohammedan fanatics" in a manner similar to the one described above, but so far all we've turned up are several different accounts with nothing that documents Pershing's involvement.