Why would a murder bring his gun to the police so they can identify him... My best guess is that the murder weapons were never registered, because most criminals don’t bother to register their weapons, or follow the law.
You’d be surprised at the number of law abiding folks who don’t register their weapons either. They follow the law as best they can but won’t take their private sales weapons down to the BATF office to be inspected.
The murderer most likely would not. If some teenager took his parents' weapon while they were away at work, and replaced it before they got home, this tactic might actually find that out. It's reaching, but they don't have much else with which to work. I'm a little concerned they're so sure it's a Glock, though. Tell-tale signs might be a bulge on the casing due to the casing being slightly unsupported towards the bottom rear of the chamber, or the mark left by the firing pin, but there are multitudes of .40 caliber pistols, and some of those casings are going to look similar from whatever weapon they're fired.