The claims against his character that the journalist makes at the beginning do not seem substantial enough to cast him as a liar.
Even more so, the parts of the story that do not add up, in the author's eyes, seem problematic but not totally unresolvable. For example, I don't think it's too farfetched to think that they may inventory the contents of the SEALs' pockets before departing on a mission.
The author of this piece also seems to imply that there is no good reason for the journalist not to reveal his sources, which is of course totally wrong, especially for something like this.
Lastly, the author totally ignores the fact that she is accusing of complicity a magazine known for the quality of its fact-checking. I would think it's safe to say the author's deception would have either have had to be astonishingly good or the new yorker to be particularly malicious for the accusations here to be true. One of those may be the case, but she should explicitly say that she is questioning the ability of the New Yorker's fact-checking team.
I guess at the end of the day, it's still worthy of questioning and investigating, but to me this article comes off as the argument of someone with an ax to grind more than an investigation.