OK here is a perspective from me ( a Texas Police Officer) as to why I have to have the gun in my hand BEFORE I will run a serial number for anyone. Every department I know of has this policy of "don't run the number unless you have the item in front of you, and you are able to seize it if it comes back stolen".
When a serial number is checked, this is what happens. A computer inquiry is routed from that department to the state & to the federal database of stolen items. The federal database is maintained by the FBI. The inquiry is either sent by the officer at a computer or by the dispatcher at a computer at the station. Only specially authorized computers can make this inquiry. The officers NAME and DEPARTMENT are on this inquiry. This activity is ALL recorded by the system.
If the number comes back to a stolen gun, the agency (say somewhere in Arizona) that entered that gun as stolen automatically gets a message (normally an instant computer message) from the national system that officer 'x' at 'xyz' police department (in Texas) just ran that serial number.
Regulations dictate that the two agencies then have "x" number of minutes to make direct contact with each other (either by phone or over the computer teletype). Details of the matter are verified and 'stolen confirmation' is either verified or declined if things don't match up.
If either agency fails to make this contact within 'x' minutes, then automatic flags go off at the state and federal levels and inquires are started by either the state or the feds as to what is going on. When it gets to that point, people can get fired and/or get charges brought on them. These regulations I refer to are the operating rules that all users of the system must agree to before being given access to the system.
The officer that checks the item for stolen is mandated to seize the item once the confirmation has been made that the item is indeed stolen. The only way to absolutely make sure it is possible to seize the item is for the officer to have physical control of it before he starts the inquiry.
The explanation you got of "we need to see it to make sure every other identifier matches up" is a partial truth. The original stolen item report will have other identifiers on it, such as model number, physical description, etc. This helps eliminate the possibilities that numbers got transposed or entered incorrectly. The department to department contact after that first computer 'hit' is the time that this is done.
LEO, NRA member, Native Texan. Shooting and hunting for over 45 years!