I'm not sure why everyone is so protective of serial numbers, honestly. I could see why a person might want to try to figure out if a second hand gun is on the up and up before buying it. We have people come into our police station with guns from time-to-time, wanting to check the serial number (as someone posted above, if the gun is stolen it's being confiscated).
There's really no need to protect the sanctity of a serial number, insofar as I can tell. A lot of people sell other property online and intentionally provide serial numbers for products that have them. Why are so many gun owners concerned about such things? I've heard the argument that was posted above, about someone else acquiring the serial number and then trying to report the gun as stolen. Frankly, I've never heard of this actually happening, and most petty criminals won't want to risk picking up a false reporting charge for doing so. I think that argument is more paranoia than a legitimate concern, honestly. Even if someone tried to report one of my guns as their own, I can easily prove ownership.
My guess is that this buyer was probably going to contact a police department to see if they'd check the serial number on the weapon. Whether the department would provide him with a clearance is another matter. Typically, I only provide a clearance on property that I have in hand. Same goes for people who call in and ask "do I have a warrant?" ... "I don't know, but if you come down here we can find out".