Even for a CIII weapon, it's not hard to get your hands on one - provided it's a legal gun and you have the thousands, yes THOUSANDS of dollars to buy one. You can pnly buy/transfer one through a specific CIII dealer, not just Joe's gun shop on the corner
You need:
ATF Form 4 (2 copies)
2 passport style pictures
Police Chief sign off on Form 4s saying you are eligible to own such a weapon in that area and you have no pending criminal charges and there are no convictions on your record.
2 FBI fingerprint cards
1 $200 Check made payable to the ATF for the tax stamp.
Provided you get all that, can pass the background check, can pay the money and wait the 45-60 days, you too can have a fully auto firearm.
It's the same process for a Short Barrelled Rifle (SBR) or Short Barrelled Shotgun (SBS)