Surely if he left for some other island the boatman/woman would know this.
There seem to be two routes to Symi from Pedi (why do I keep thinking of feet here, sorry...). One overland, and one longer one partly overland and then along the coast.
As others have said, the concentration of the search was from the beach to Pedi, whereas it appears the search should have been from Pedi to Symi, but the beach was the last sighting by his wife/companions so it made sense at the time.
I'm puzzled as to why the CCTV wasn't identified initially, but probably because the search was focused in the wrong place at first, and then when there was no result it moved to Pedi, and there he was found on CCTV.
No one knows what happened, but the longer time goes on, you'd have to think the worst, but at the same time hope for the best too.