It's going too far to say that Pershing definitely was responsible, but since Pershing did write about the story in his book, the president isn't entirely wrong this time.
Look through my posts. I posted three different links to three different sources that corroborate the burying them with pigs story. One of them is the New York times in 1923.
From the Daily Mail:
But the reference to Gen. John ‘Black Jack’ Pershing inserted Trump into the day’s most riveting news story in a way his White House could come to regret.
There was criticism of the president for his use of it, with CNN anchor Jake Tapper calling it a ‘lie’.
Trump’s anecdote is a fictional story that he told in South Carolina ahead of the state’s Republican presidential primary in February 2016.
The story centers on Pershing’s supposed killing of prisoners during the early 1900s when his army was targeted by an insurgent guerrilla campaign of Muslim ‘Juramentados’ who targeted Christians with gruesome sword attacks.
Pershing was governor of the Philippines’ Moro Province at the time.
‘They were having terrorism problems, just like we do,’ Trump said. ‘He caught 50 terrorists that did tremendous damage and killed many people and he took the 50 terrorists and he took 50 men and he dipped 50 bullets in pig’s blood.’
‘And he had his men load his rifles, and he lined up the 50 people, and they shot 49 of those people, and the 50th person, he said; ‘You go back to your people and you tell them what happened’.’
‘And for 25 years,’ Trump ended, ‘there wasn’t a problem. For 25 years there wasn’t a problem. Okay? Twenty-five years, there wasn’t a problem. So we better start getting tough!’
On Thursday Trump upped Pershing’s effectiveness by 10 years, to 35. Problematically for him, the bullets-in-pigs-blood episode never happened.