A Class 3 license is a license that a dealer obtains to sell Title II Firearms. Many individuals incorrectly confuse the terms Class 3 and Title II. We even see some lawyers making the same mistake. Class 3 SOT is a license to sell. Title II is classification of firearm that a Class 3 SOT may sell.
Title II firearms include silencers, short barrel rifles or shotguns, machine guns, AOWs and destructive devices.
So the answer is no! You do not need a Class 3 license to buy a silencer or other Title II firearm unless you are a dealer and wanting to purchase them for resale. If your documents do not use the correct terms, the people who wrote them may not understand the NFA, ATF and issues relating to the purchase, possession, transfer, and use of Title II firearms.