On May 20, 2009, four Muslim men from upstate Newburgh were arrested by the FBI and charged with plotting to bomb two Jewish synagogues in The Bronx and shoot missiles at military supply planes at Stewart International Airport.

The FBI and NYPD claimed they caught the infamous “Newburgh Four” red-handed. But was the sting really a setup, and were the men more guilty of simple greed than terrorism?

Those are the questions “The Newburgh Sting,” an HBO documentary premiering Monday at 9 p.m., seeks to answer. It was directed and produced by Emmy Award winners Kate Davis and David Heilbroner.

When Pakistani-born Shahed Hussain first showed up at the Masjid al-Ikhlas mosque 60 miles north of New York City in spring 2008, worshippers took note of his fine cars and fancy clothes — much of it provided by the FBI.

Hussain, convicted of fraud for helping illegal aliens get driver’s licenses and desperately trying to avoid deportation, had turned FBI informant in 2002.

Hussain’s flash attracted the attention of James Cromitie, a Walmart employee and drug dealer. Conversations of hypothetical situations quickly turned into discussions of a plot to bomb synagogues in the name of Allah.

At Hussain’s urging, Cromitie recruited three others: David Williams, a part-time student with a past drug rap who needed cash to get treatment for his brother’s liver cancer; Payen, a Haitian immigrant who Cromitie believed was “a little slow”; and Onta Williams, a drug dealer who had served time. None of the four men, all broke, even owned a car.

Hussain promised $250,000 for a successful mission. All four men agreed to help under one condition:

“We don’t want to hurt nobody,” David Williams is heard telling Hussain on FBI hidden-video footage “We want to just destroy property. We don’t want to take no lives.”

The foiled terror plot was trumpeted as a “textbook example of how a major investigation should be conducted” by then-Police Commissioner Ray Kelly.

But Mike German, a former FBI agent not involved in the case, told the filmmakers the sting turned the men into people they were not.

“Were they the best people in society? No,” he said. “But they weren’t terrorists, and this government operation over the course of the year was specifically designed to turn them into terrorists.”