Yes, there is an issue with this. You must obtain approval in writing from BATFE prior to taking your NFA weapon into another state. There is a form which can be faxed to BATFE. If you travel frequently to other states, you can list the destination address and prepare the form to cover an entire year.
The only exception involves C&R classified NFA weapons, if you possess a C&R (Curio & Relic) category of Federal Firearms license. No advance approval is necessary for C&R weapons.
You must only get permission to travel with machineguns, SBR's or SBS's or DDs. The others (silencers, AOWs) don't need permission to travel. The form is 5320.20
The information pertaining to suppressors is indeed correct. The last form 5320 I filed with BATFE is several years old. However, it states any destructive device, machine gun, short barreled rifle or short barrelled shotgun is required to have advance approval under Section 922(a)(4) of Title 18 and Section 178.28, title 27, CFR.
Not trying to be smart here, but the facts are important.