The logic behind that declaration is pretty simple. The Falcons have their full complement of draft picks for the first time since 2011, and they have real holes they need to use those draft picks to fill. We can argue about whether there are improvements to be had in the secondary, but it was clearly one of the team's stronger units in 2012. Trading for Revis would cost, at minimum, a first round pick, and he is coming off a major injury.
Yet it's still a powerful idea, this potential trade for arguably the league's best cornerback. And then Revis had to go and make it more interesting by wearing a Falcons hat recently.
It's not entirely unheard of for players to wear hats belonging to teams in different cities, but it tends to be teams from other sports. For a player about to be traded, it could be a fashion statement or a statement of preference. It could be extremely meaningful or entirely meaningless. We could drive ourselves mad just thinking about it.
Even if Revis is sending a signal, there's no guarantee the Falcons are going to see it and squeal that Revis likes them. As I've already mentioned, the cost here is huge. But you can bet that Thomas Dimitroff is calling the run-down rotary phones at Jets HQ just to inquire, because this is the man who convinced the Eagles to trade Asante Samuel to the Falcons for a seventh round pick.
Ultimately, it probably means nothing. But knowing the Falcons' willingness to gamble and considering the sheer oddity of wearing a Falcons hat for Revis, I wouldn't say it's impossible.