When I tried to use ～かねない to express my own feeling about a situation, I was told by a native that it sounds incorrect and strange. However, ～かねる is appropriate and fine. For example, this is the impression I get of what is going on.
(the speaker thinks it's hard to believe he's telling the truth)
(the speaker thinks he's probably not telling the truth, yet others think he is)
However, I was told that ～かねない cannot directly refer to the speaker's opinion, but to can refer to someone else. For the second example, is it true that you must directly reference a different party? Why is that?