See, I think one of three scenarios might have happened:

• Luigi didn't do it. He was framed and set up because out of the hundreds of prank tips, this guy looked "close enough."
• Luigi did it, but the evidence was made up to make the case solid and the police look competent. Luigi wasn't stupid, but he's boned anyway.
• Luigi did it, and he really was that stupid.

As a writer, one of the aggravating tropes we have to follow is, "make the story believable," when reality sometimes doesn't align with "a good story." Some criminals are really that stupid, and some armchair theory, based on decades of movies, books, and TV shows, you expect "hey, this is what they SHOULD have done is." And they didn't. It's like when a chessmaster has to watch complete amateurs play chess. "Obvious strategies" are ignored, and basically both players are just not thinking past their last move.