The reasoning isn't bad, if you assume (as I do not) the anonymous author didn't intentionally obfuscate. Herring's conclusion:
I am of the opinion that this is likely an Obama holdover (of which there are still more than a hundred in the employ of the White House alone) writing as if he were in fact a disaffected member of the Trump inner circle when he is in truth a bitter refusenik still stinging from the rejection of November last.For sure all such holdovers will come under extreme scrutiny since 'anonymous' broke into print. It's not clear why Trump hasn't dumped them all; even corporate CEOs normally clean house when brought in from the outside.
I think I know why the NYT kept it anonymous. "Disgruntled Obama holdover" doesn't carry the same cachet as "anonymous senior member of the administration."
If all this analysis does is prompt a denial from the NYT, that denial will provide another data point. Hat tip to Lucianne.com for the link.