If you watch enough true crime, you come to understand that this is how it is with murderers a lot of the time, to wit: they're usually not masterminds. Asking questions that start with "but who would be dumb enough to [X]" will usually get you an answer along the lines of "most killers," because most people are not the 190-IQ serial killers of primetime TV. They are enraged, and probably not very bright. Would a novelist write a crime like this? No. Do people give themselves away like this all the time? Sure do.