After watching the Doctor Who episode Listen I was left with the impression that it was the Doctor's own nightmares and fears which led him to believe there was a creature perfectly evolved for hiding.
This is most likely caused by...
his encounter with Clara on Gallifrey. She hid under the bed and instinctively grabbed his leg when he was a child. This explains why he's so fascinated by the dream.
He's so used to battling monsters and aliens that he's very likely to believe such a creature is possible - he's using his own knowledge and experience to back up a common fear.
However, if all the strange noises and feelings were in fact simply people's subconscious then what was the very visible thing under the Rupert's bed?