MOO Because he communicated something to them that convinced them he was suicidal? Because the circus outside was gaining steam and they thought it would stop if they reported he wasn't in the home anymore? Because they got the all clear from the professionals they hired to get him into a 3rd world country? Because they had all the fake leads in place that would lead LE on a merry goose chase in the Reserve? Because the mother had a momentary flash of grief over the loss of GP and called LE to come clean?
Anyone want to add some more?
Yes. BL uses the same home address as his parents, and was known to be staying/sleeping there. Without explanation, he goes for a day hike and does not return. They wait, do not hear from him, become fearful for many reasons and call police. He was, at that point, missing from his home address and incommunicado with all known friends and family. So naturally, LE would take a missing persons report.
Everything else you're hypothesizing could also be true. I can add some more. They might not have had to hire professionals, they may have used friends and family members. The goal of the subterfuge would be to make LE think he perished in the swamp or killed himself.
For all we know, he walked rapidly along the path beneath the power lines to the other side and hopped in someone's car. Made a stop at a prearranged hotel (car driver has the key), changes his appearance, is taken to a harbor, where someone has a boat.
Pleasure cruise, hitting a port in a place where a pleasure craft would spend a day or three at harbor, having a BBQ (no one officially goes ashore, it's like camping), but chosen for reasons known only to the organizers of this escape.
Or...BL could have managed quite a bit on his own (which I think was more his style). By walking a fair distance without being seen, and then staging a US based disappearance.
It's interesting that his parents say they think he's still alive. They know him better than we do.
In that case, I'll imagine he's heading back out west, perhaps with a vehicle procured by family. He won't go to the AT, he can read. And he won't go too far north (soon it will be too cold). He's seen some of the most wide open spaces, and so many styles of living on the road he could try. Wants to go it alone.