Whether it scans is just a question of how much effort goes into any given investigation, surely?

I mean, if one fed says "I'm a reporter", and a second says the same but also has AP business cards, and a third also has an authentic-looking AP badge with his photo and the name of a real AP journalist, I don't guess there's any bright line between those things. Once the feds decide to impersonate a journalist they could be arbitrarily convincing about it, couldn't they?

If I wanted to leak something, I would choose the reporter.

I would probably go to a library and evaluate the writings of several reporters, and choose from there.

I would then figure out how to identify the chosen reporter using materials that they did not provide to me.

I would not rely on my ability to authenticate an AP badge.

I don't think any of that is particularly sophisticated, so I would expect many leakers to at least take that first step (and hopefully they would usually see the problem with using information provided by the reporter to evaluate the identity of the reporter).

Your extrapolating from your own course of thought and actions and assuming that everyone in the world makes similar enough decisions as you do that it's not worth considering alternate scenarios.

Not everyone has the luxury of deciding if some proof is good enough in a a consequence free thought experiment where they can also shape the constraints. IRL constraints and persuasion tactics shift the ability to verify, and someone with legal considerations can't afford to be wrong even once. It shifts the decision making process in such a way that the fact "cops have posed as reporters" plus an abundance of caution means nobody talks to reporters. Exactly the circumstances the AP is afraid of.

We are talking about people choosing to commit a federal crime out of the belief that it serves the greater good. If they aren't capable of being cautious, I first don't want them handling sensitive government information, and second, I don't want them making the decision to share it with the public.

Sure, but don't you see that your personal opinions don't apply directly to someone else leaking information, or more generally, chilling effects on things that aren't federal crimes?

I don't think this issue particularly concerns leakers. A typical journalist spends most of their time contacting people to ask questions, and it would affect the functioning of the press if everyone had reason to suspect it might actually be the FBI calling. That's where I'd think the chilling effect comes in.

Edit: sorry, I'd overlooked that the top post in the thread was specific to leakers.