In US law, there is a nuance between Copyright and Trademark.
> Drawing a copy of a copyrighted picture from memory, and then distributing that copy
Would not necessarily be copyright infringement (it depends on a judge). For example, why Taylor Swift is able to re-record her music (the copyright is owned by a recording studio), as is, and can distribute the new version as "Taylor's Version" because she owns the copyright on the new version.
> (A logo may not be enough of a creative work to be copyrightable, but I assume that's not what you're getting at).
A logo is actually MORE protectable, through Trademark. Trademark is significantly MORE protected than Copyright.
In your example, if someone draws from memory a logo, they actually own the copyright, but it is still Trademark infringement and the trademark owner will be protected.