Parthenius' version doesn't say a whole lot about Narcissus being a little bastard. It says one line:

He had a cruel heart, and hated all of them,

That's not really a source, it's a completely subjective judgement. As a rule, I tend not to trust gossip about a person that says they're bad, but not why. Because we don't really know why Parthenius judged Narcissus. Conon said Narcissus was bad because he was asexual, so I'll hazard a guess that Parthenius may have agreed. Because it's literally the only clue we have about why Parthenius insulted Narcissus.