I've processed government requests at a FinTech before. Some are pretty good and there are bespoke channels for them so that you can be sure their genuine. Other are literally random emails you get that you are required to reply to, many of them demanding information to be sent in the clear. We always declined to reply to those even though we legally had to, we offered them to set up PGP if they wanted the data via email, or we offered other secure mechanisms for them. Most of these (who I know were from real agencies) stopped asking for the data once we stood firm that we could only deliver it over an encrypted channel.
Note: This is now 5+ years ago so things have probably changed since then.
I am not surprised at all that fake requests receive real responses, happens probably way more than anyone thinks.
For a while, Comcast/XFinity required the FBI to show up at their offices and present their badge. No emails. But I'm guessing that's changed. At the very least, it's also possible to forge a badge.