No, the linked article specifically states that union literature is not given any special treatment, at all. Companies can indeed restrict it from being spread, even in break rooms, if: 1) not spreading materials in the break room is necessary to maintain work productivity, and 2) all other materials are treated equally and are also not allowed to be distributed in break rooms.
edit: the above is actually for union discussions in break rooms. It's not clear if the same rules apply for literature in break rooms, but given that other parts of the article specifically call out that all literature must be treated equal in other areas (ie not break rooms), I'm not convinced that it doesn't apply.
The stance of the NLRB regarding union materials is that it is explicitly not given any special treatment, neither in regards to protecting its spread, nor in regards to preventing its spread. It must always be treated equally to materials on other topics: either everything is banned, including union materials, or nothing is banned, also including union materials.