This is another one of those issues where the answer is not can you do but what should you do. Technically, you do not have to have a copy of your Form 1 or Form 4 for anyone other than the Attorney General, the ATF or an agent or investigator upon request.
Some recent case law has stated that a police officer is not an investigator or agent or the ATF and as such has no right to request to see your ATF form. I cannot believe the amount of money and or the risk that the individual took when a copy of the document on your cell phone or in your gun bag would have avoided the issue. In addition, there is nothing to state that a judge in your state or where you are asked for the paperwork would rule the same way.
The NFA requires that a person possessing a firearm registered in the National Firearms Registration and Transfer Record (NFRTR) retains proof of registration which must be made available to the Attorney General, specifically an ATF agent or investigator, upon request.