Ironicallly, it's actually iamleppert's post that seems to be misrepresenting things.
Firstly, the Dalio doesn't say "trust me" anywhere. The word trust doesn't appear in it at all, and the closest it gets semantically is the closing paragraph where he says:
You are now faced with a choice. You can believe my account of what’s happening or The Wall Street Journal’s. What you do is up to you.
The story he's taking argument with is about inter-personal relationships and subjective claims so it's hard to prove anything about it objectively. But nonetheless, he actually has "provided any kind of evidence or arguments to support any of his other hyperbolic claims of systemic problems in journalism of the WSJ".
Specifically this: Dalio states that one of the journalists applied for a job at his company and was rejected, the WSJ knew that, and kept him on the story anyway. That would create a problematic conflict of interest (plus it seems Bridgewater and this specific journalist have a long running fight of some sort). The claim is uncheckable directly but the journalist has replied to Dalio's post with nothing more than a link to his article and "Happy Sunday". If such a very specific and problematic accusation were false, presumably he'd dispute that.
To me that's sufficient to support his claim of bad journalism at the WSJ. It's not a claim hyperbolic if they're assigning failed job candidates to cover a company.
He also disputes the other claims but both the WSJ and his position seem very subjective, it's all about to what extent he really controls the firm and whether there have been internal fights or not. I don't see any way to judge who's right there. You'd have to believe in the WSJ's process for finding the truth to take a side here, but as they rely entirely on anonymous sources and already failed step 1 "no conflicts of interest", I don't see why we should automatically assume the WSJ story is true here.
You're right in that he didn't say "Trust me" but he did say a trust-seeking analogous of:
"I can assure you that that is not true and that if it was true, I’d tell you it was true."
The definition of assure is: "tell someone something positively or confidently to dispel any doubts they may have."
Note the definition of trust: "firm belief in the reliability, truth, ability, or strength of someone or something."
"I can assure you" presented without any assurances or facts otherwise in this context is simply another form of "Trust me".
In any event, without mincing words, the WSJ article presenting some very concrete evidence that his business is both a mess internally and by the numbers isn't delivering compared to a simple index fund. Why didn't he address this in his post if it was untrue? The WSJ even presented a graph with data to back up their claims on rate of returns. I verified the last years numbers (admittedly with a quick Google search, but two other sources seem to have similar conclusions).