They looked at Billie's car, not Shawn's truck to my knowledge.
Did he have a truck at that point?
If he was their POI why would they search her car and not his? That does not make sense, especially since only one of them was driving at that time and presumably that meant there was only one vehicle.
I have been giving this some thought, to try and figure out why LE was behaving the way it was in the face of what they were saying publically.
Most of what we know about the case is information from the affidavits written up around January 7th. At that time they were gunning for SA. One of those warrants was for the phone records for the cell phone that was left at the Dunn residence on the day HD disappeared. My guess is when they got those records, they showed that HD was there that day, and, combined with witnesses backing up SA's account of where he was that day, they no longer had probable cause to do any further warrants directed at SA.
The lack of any further HD related warrants directed at SA, or places associated with him, implies that the investigation as it stood on the 7th turned out to be a dead end. Otherwise they would have executed additional warrants.
The only wiggle room they could still exploit in terms of probable cause was the child *advertiser censored* theory, as far fetched as that was. The later warrants executed at the GM's house and on SA's person were fishing expeditions in the hope that they might find something else in the process. After the warrant on the GM's house they did not find anything and that angle fizzled as well.
I think that would explain why no further warrants were executed even though they were naming him as a POI. They had a hunch he could be involved, but after the 7th they had no evidence and his account of the day largely checked out on further investigation. That left them with nothing other than a fixation on him as the POI.
I think it is entirely possible that they were looking at the wrong people/places entirely in the investigation, and developed tunnel vision that resulted in them missing what really happened. If that is true, then after all this time whoever is responsible for what happened to HD is probably going to get away with it. So what really happened, and what was HD doing that day?