Commissario
The police etc would only spend a limited amount of time and resources on it, they don't have the ability or inclination to spend months looking so typically have an intensive search for a few days when the chances of survival are high, but then it becomes a lower priority and they might only follow up on potential sightings.
The boyfriend wants to know what happened, had the skills and presumably time and money, so spends the time looking long after the official search has finished (and quite likely covering at ground level areas that might have been looked at from the air*).
It's not overly surprising and similar things have happened many times in the past because for for the police it's most likely an accident and one incident of potentially hundreds they're dealing with at any one time, for the BF it becomes a bit of an obsession and the focus of his life.
There are dozens/hundreds of hikers and climbers whose bodies have not been found, or found only years later often near where they went missing but no one spotted them in the initial intensive searches and it's either been chance that a random hiker found them, or the result of someone who has decided to try and find them and spend the time looking (sometimes obsessively, sometimes at least partly as it's an excuse to enjoy their hobby).
I think it was a couple of years ago they found the site of a light aircraft crash in an American mountain/hiking area after several years because a local had taken an interest in it and had been looking whilst on his hikes, this was despite the fact that there was an an intensive search and rescue effort at the time and they were looking for something much larger than a single body.
*And it's extremely easy to miss something even at relatively close range if you're at the wrong angle, even from ground level (hence "fingertip" searches with lines off people a short distance apart in more hospitable grounds than a mountainside), let alone from the air.
