Agree about it might send out a message to others. But I don't think this transfer is a very good example of the initial point. If Chelsea were desperate to keep Mata and United came in and plucked him away it would say a lot about United's pull in the transfer market, but under the circumstances that it happened it doesn't really show that.
Of course though, a top player signing could turn the heads of other players to join.
I think the tweet has the right sentiment, but overstates the impact. Still a big point has been made. Pellegrini and Wenger both complaining. One would think they might actually be worried about United...