NSLs aren't signed by "The FBI", but rather some Agent of the FBI, which includes their case number and contact information. Even if one had to cold call the FBI operator, they could probably ask for the investigator in charge of case "X1234" and get whomever they needed that had clearance to discuss the issue.
If someone forged an NSL, it would be arguably trivial to verify it's authenticity by doing a number of things, including walking into a local FBI office and asking to speak to someone about the case number, which is public enough information within the confines of the agency to get you someone who can talk about the case without having to describe the specifics of the letter over a phone to someone who might leak that information resulting in your arrest.
> speak to someone about the case number, which is public enough information within the confines of the agency
I have absolutely NO idea how you reach that conclusion. I know that legal arguments have been made for suppressing every single word of a NSL, and that even admitting the existence of the NSL is specifically prohibited by the law.
What makes you think that this query would not be a violation of the law?
Well, the WP article on NSLs has an EFF-sourced minimally blacked-out example of an NSL, which explicitly states "[blacked out communication details] or through use of a delivery service or secure fax...", and while there is an entreaty to not disclose it through routine mail or phone, it would seem there are mechanisms (including, presumably, asking your attorney to file paperwork about it and seeing if it gets sealed so fast your head spins) to communicate about it.
Imagine delivering a fake NSL that's forged using a random case-number that happens to correspond to a real, active, and classified investigation, though. (Not even necessarily one that ever issued an NSL.) You'd ask them to talk to you about the case number, and then they'd completely clam up, because it is a case but it's one that doesn't involve you at all, so they don't want to admit of its existence to you. Kafka-esque results.
If someone forged an NSL, it would be arguably trivial to verify it's authenticity by doing a number of things, including walking into a local FBI office and asking to speak to someone about the case number, which is public enough information within the confines of the agency to get you someone who can talk about the case without having to describe the specifics of the letter over a phone to someone who might leak that information resulting in your arrest.