But isn't it valid to doubt someone's belief if they don't follow up on it with some kind of action?
If I say, I believe I can get a really well paying job if I go to Company X tomorrow and apply there, and then I spend the next week in front of my TV instead, wouldn't you doubt that I really want this job?
Not saying the parents spend their time in front of the TV, this is just an example.
I think it's valid to assume they don't believe in an abduction anymore - for whatever reasons. It does not mean they necessarily believe he died at the campsite. Plus, the emphasis is on 'assume'. I wouldn't go as far as saying it is fact or sure.
jmo