If you saw a video of your daughter, an hour or two before she was brutally slaughtered, and in that video a guy followed her when she left the location, and the police told you he was ruled out the same day her body was found, wouldn't you want to know what sort of alibi he had? They have video of him going home? And/or witnesses that prove to you he definitely could not be the killer? Normal questions to think about in this scenario, and now combine it with SG's lack of confidence in LE which he has clearly explained the reasons for... The cherry on this sundae of psychological torture for SG is the fact that unproven and likely totally false rumors are circulating online, in the media, etc that this guy in the video didn't give DNA and left the country.
He has not been approaching his issues with LE and his need for more info in a constructive way. However, he's literally in emotional hell right now. If he chooses a good PI, I think that PI will be able to find and provide SG with enough info about certain aspects of the investigation to ease his mind that people who have been cleared have rock solid alibis, that no stone is left unturned, etc.
People are being rather vicious about SG. I get that he's actually hurting the investigation the way he's been going about it, but hell man, he's not doing it on purpose and he deserves some empathy and understanding.
Again, assuming he gets a good PI, I think SG's media appearances will be limited, and he will be prepped to convey appropriate info that doesn't compromise the investigation in a more coherent way. He needs help navigating this, and I hope he has hired someone great to help him.