With the understanding that I am not giving you legal advice and I am not your attorney, my view (and what I advise my clients) is this:
My trusts have a Schedule A where you list all of the trust's property. I also provide clients with an "assignment of property" form that they can use for anything that they place into the trust. All items owned by the trust must be placed into the Schedule A. Legally speaking, none of them are absolutely required to have an "assignment of property."
What the "assignment of property" form does is create a legal paper trail so that if there is ever any question of whether the trust owns an item or whether you retain an individual ownership interest in it, that question is answered by you legally declaring that you're giving all interest in the property to the trust.
With that said, I really can't imagine many situations in which that legal question would truly arise and that a court would really question it. It's just that while cars have titles and houses have deeds, firearms have no record of ownership. The assignment of property creates one.
So my answer, for what it's worth, is that you can do an assignment of property even for an item on a Form 4, just so that it's clear that any individual ownership interest you may have had in the item has been transferred/granted to the trust. This might be a comfort to you if you pay for the item with "your" money instead of the "the trust's" money. (I put those in quotes because I've never bought into the idea that a trust must have a bank account--the grantor of a trust is legally allowed to put property into a trust, so I see no problem with the grantor of a trust paying for trust property or tax stamps with his own funds.)
The other, somewhat related, question that I often get from clients is whether to list a piece of property on the Schedule A before the Form 4 is approved. My answer is always yes. That's because the Form 4 is merely a request for the ATF to approve a physical transfer of the firearm from one person to another. If you have already paid for your NFA firearm at the dealer, you have an ownership interest in it, even if you are not allowed to legally possess it yet. Therefore it is proper to list it as an asset of the trust even before you take physical possession.
I'm sorry if that was a rambling answer, but hopefully it clarifies matters for you.
Aaron