The problem with this memo is that it conflates the use of "tweet" as a noun (useful and precise) with its use as a verb (much too casual for formal use). I agree with the author as to the latter but not as to the former.

There are some contexts in which a certain level of formality helps keep an elevated tone that suits the forum. I think the New York Times is one such forum. It has a long tradition of maintaining "standard English" and at least some significant portion of its reader base might be jarred should its reporters suddenly lapse into forms of expression that depart sharply from that standard.

"Tweet," though, at least when used as a noun, is really what I would call a "term of art," that is, a form of expression that captures a range of attributes not easily otherwise expressed except in wordy or imprecise ways.

Casual-sounding as it may be, it is the one word that describes perfectly the form of short message that one transmits to those to whom one is connected on the Twitter platform.

Thus, in one word, it describes:

1. The type of platform on which the message was sent (Twitter).

2. The fact that is 140 or fewer characters and hence either a short phrase, single sentence or two, or other informal expression of thought about a subject (as opposed to any form of carefully developed argument or expositional form of expression).

3. The fact that it is sent originally to those who are "following" such the sender, who may be but likely are not intimate with the sender (Twitter being a very public platform).

4. The fact that such a message can easily be spread virally by those followers to others who are in turn "following" them or can be linked to from a wide variety of sources from all across the web.

Given that the paper's own (highly skilled) writers had used it 18 times within just the past month confirms this. "Tweet" (used as a noun) is a good, solid word - precise, accurate, pithy, and almost certainly carries a meaning that is well known to anyone who knows what Twitter is. I don't think it has a good substitute that is not either wordy or imprecise compared to the word itself. That is why it is a useful term of art. For that reason, it makes no sense to dissuade use of "tweet" as a noun, and I think the memo author is plain wrong on this.

I would side with him, though, when it comes to "tweet" as a verb (as in, "I will tweet you"). This is much too casual for a formal publication such as the times. There is of course nothing wrong as such with this verb, and the issue is strictly one of tone. But the author is right that, in terms of tone, the word is misplaced in this particular publication.

Edit: point well taken, ismarc - a different rationale from that of the memo writer but a sound point about avoiding reader confusion, at least until the term acquires broader general usage.