I've made copies and one set stays in the truck. Out of respect of range/land owners, I inform them that I will be using an NFA item and offer to show them my paperwork. Most don't care and don't want to see it. One range I go to a lot wanted to make sure everything was legal just because there is always a fed or state LE on the range training or qualifying. The ATF FAQ says the approved paperwork must be presented to any ATF AGENT who asks for it. Doesn't say "to anyone who asks for it". I'm not going to get into it with anyone over my own legal items, so I'm either going to leave or be up front about it. If their ignorance is strong in not going to even entertain that shit They don't need my business.
On the flip side if I owned a range or facility that is my livelihood I'm not going to chance illegal items being use at my place. So it would be my policy for people to bring their paperwork with them. It CYA if LE gets involved.