interesting read and hope that it ends the "best way possible" for you...
but, while reading it, a few recent experiences of my own came to mind.
Last month a brand new member posted sold for a few domains of mine. Just to do some background checking while deciding on how best to finalize the deal with them, I did a whois on the domain they were using for email. Was brand new, no address,state etc, just a phone number. Well, thought that was odd so googled the # and.... was a customer service number for the city of San Jose. When I confronted him about it he said he wasn't claiming to BE from that organization, was just "borrowing" that number to: "cover my identity for public situation as I'm a domainder, please understand"....
Another odd one recently was an email on a Sunday from someone claiming that they recently purchased a website from me but had not received anything etc and were wondering what was up. They weren't sure which email they used for the transaction, but listed a phone number and an email that "might" have been used, which a google search revealed were for a business, but that I also found in a marketing contacts compilation via google.
So... goes without saying but anyone can pretend/claim to be anyone, if nothing else just to waste your time. Maybe seeing if you will reply and go from there, maybe a clear agenda. They could even send the email from a strangers email addy, they won't get the reply but if they are in it for kicks, or to potentially cause you trouble when you reply, then they really don't have to get the reply.... just putting the ball in motion.
I sure hope the offer is legit (if you are satisfied with it) but must say that, at least based on the single quote that you shared and not knowing the domain, it seems more than "odd" to me to be approached in this way from a dept like them for a couple reasons:
1) if it was a domain that they had targeted to take down/acquire/whatever, they could most likely do it without having to pay you a penny.
2) if they DID want to buy it for a project, then I imagine they would either do it "anonymously" through a broker and not expose their identity OR they would be very up front about who they are in a MUCH more transparent, polite and professional way, make their offer and leave it to you to gauge whether it was worth the time, hoops and bureaucratic hurdles to attempt to get a higher price approved or blow the sale.
As was mentioned before, based on what you shared the person that sent you the email did not directly CLAIM to be from that agency, but used contact info that is "connected" to it..... maybe it is someone hoping you won't bother calling the number, or would be intimidated if you did, or maybe it is someone that is just wanting to get a laugh and have you send a "reply" email to that email address and someone (if it goes through) gets it and wonders "what the HECK?!" since they never sent the original inquiry to begin with and are now getting spammed with a "negotiation" email for a domain they never even thought about, let alone inquired about lol.
But, hope the offer is legit and it ends well for you. Good luck! SP