u/CptBuck discussed an incident from the Philippines that has some resemblance to the debunked Pershing account here.

As to possible connections to the Indian rebellion of 1857: the story of the greased cartridges was fairly well known and was mentioned in a number of books on the campaign of the sort that professional military men might have read, but I am not aware of any proof of a direct link between that story and the Philippines.

With regard to the 1857 rebellion, it's worth mentioning, first, that the account usually given of the introduction of cartridges greased in animal fat is exaggerated; it was certainly intended to introduce munitions produced in this way, and some sepoys were issued them in trials, but there are no records of Indian troops actually being required to load their guns using the tainted cartridges. That said, the British were perfectly aware of the potency of religious taboos among those who had risen against them, and some of the atrocities they committed in the aftermath of the rebellion exploited them. Most notoriously, when Colonel James Neill and his men reached the Bibighar, a house in Kanpur (Cawnpore) where rebels had murdered a large number of British women and children, they rounded up a number of local Brahmins who had had nothing to do with the massacre and forced them to clean bloodstains found at the scene on hands and knees with their tongues, an act that broke their caste and reduced them to the level of Untouchables. The Brahmins were then executed.