I personally don't think he did it. He could easily be a grifter trying to take credit for a very popular act. There's no shortage of those. All you'd need to do:

• Walk into a public place with a bag of somewhat incriminating items, but nothing that's linked to the actual crime scene.
• Arouse enough suspicion to get the cops called on you. Being a white guy with black hair and a hoodie is not enough for someone to call the cops on you, I have no idea why people believe that was enough for a McD's employee to call the cops.
• Claim credit for the shooting to the cops.
• Bonus points - Have a social media history praising similar actions.

The altoona cops then forwarded this to the NYPD, who were desperate to pin this on someone, after they messed up and let the shooter slip through their fingers. Out of the all the tips, this was the best one they'd gotten so far, so they're running with it now.

This also explains why Luigi's taking credit for some, but not all of the claims the police made (especially about the money he was supposedly carrying).