Finally got to watch this, for the most part I 100% believed the parents innocent, the fathers attitude I can understand I think the laughing was because of the disbelief, and even more so they now in their 80s.
As for the mother leaving him at the toilets, I think he was actually very independent and didn't need 24hr care as he would return home from the pub and was actively looking for work, I started to doubt towards the end when they was told the Anonymous person had come forward, they seemed to take that badly instead of thinking it was a positive.
I came away from it thinking it could be suicide (due to his failure to find work) or harm by someone local they didn't know he talked to, due to the sightings after he went missing, but then I get confused again as of your 1st thought, only one small mention of the sister.