I just found an old draft post dating from last year's research into animal minds. I can't remember how I was wanting to finish it off, so I'll simply reproduce it as is. (I think it's interesting enough, despite the feel of incompleteness.)
To take a neat example from Dennett's The Intentional Stance (p.270): Experimenters managed to "frame" a particular vervet-monkey as a "boy who cried wolf". They recorded his warning cry, and then played it back to the group in inappropriate situations, until they became 'habituated' to it and no longer payed attention. This much can be explained behaviouristically. But, importantly, the habituated call is apparently "synonymous" to another (quite different sounding) call. And the other monkeys also ignored the framed monkey when he tried to give calls of this other type. As Dennett explains it, the framed vervet can "lose credibility with the group on a particular topic, thanks to being "framed" by experimenters."
One natural explanation of this behaviour appeals to higher-order intentionality, i.e. that the other vervets believe the framed monkey is intending to mislead them on the particular topic. Though perhaps that's still too rich an interpretation. They might merely believe he is unreliable on that topic.