Facebook’s stock dropped 2.9% in its first minutes of trading this morning. Investors were likely responding to a report in the New York Post that Instagram, the photo-sharing that Facebook acquired this year, “may have shed nearly a quarter of its daily active users” after changes to its terms of service rankled users earlier this month.

But the Post is flat-out wrong.

The story cites AppData, which tracks usage of Facebook applications like FarmVille. Some users have connected their Instagram and Facebook accounts in a way that would show up in AppData’s metrics, but most have not. So when the Post says, “Instagram, which peaked at 16.4 million active daily users the week it rolled out its policy change, had fallen to 12.4 million as of yesterday,” it’s only talking about a subset of Instagram users.

This subset might be representative, but it might not. The claim that Instagram has lost a quarter of its users isn’t supported by this data.

But more to the point, the drop in active daily users of Instagram’s application on Facebook occurred between Dec. 23 and Dec. 25, according to AppData. (Look for yourself!) Instagram released its new terms of use on Dec. 17, igniting controversy almost immediately, but AppData doesn’t show any significant decline in usage until Christmas.

It’s not clear what caused the drop, but the Post is misleading readers when it pegs the drop to controversy over the new terms of use. Monthly and weekly active users of Instagram’s Facebook application, meanwhile, continue to rise according to AppData.

None of which is meant to apologize for Facebook and Instagram, which was forced to retreat from the new terms after objections to its most ambitious claims, like the ability to sell users’ photos without compensation. Instagram said that clause was misinterpreted, but it seemed like an overreach that is all too common at Facebook.

Still, the idea that Instagram users are fleeing the service en masse doesn’t hold up to a gut check, and it certainly isn’t supported by the Post story, which has been regurgitated this morning on CNBC, Bloomberg TV, the Wall Street Journal, and elsewhere. Facebook’s stock is recovering as I write this, so perhaps investors are wising up to this specious claim, as well.