Yes, they will eventually ascertain the truth, but perhaps not until some jihadi screaming "Allahu akbar" breaks down the front door of their homes and starts shooting.
From the Daily Mail:
Police are investigating a fake Facebook advert which offered free food at the McDonald's where a gunman killed the first of his nine victims.
Munich was in lockdown for a major police operation around the city's Olympic Park, after the 18-year-old Iranian opened fire at the fast food restaurant, before targeting shoppers in a busy mall in the district of Moosach.
The killer's body has been found half a mile from the scene after he reportedly turned the gun on himself. Police now believe he may have acted alone, after they initially went in search of three gunmen yesterday.
And at a press conference at 2.30am local time today, Munich Police President Hubertus Andrae confirmed the force were probing a Facebook page which was offering free food at the McDonald's at the same time the gunman began his shooting spree.