If that is Washington, DC, you are right. There is a total ban on Full Auto firearms ownership. I don't know the law in Washington state, but check with a lawyer or find a dealer in automatic weapons.
Basically, Federal law does not ban ownership or purchase of FA weapons. It does require 1) a $200 tax on each transfer, 2) filling out forms with fingerprints and photo and 3) the signature of the local chief law enforcement officer that ownership will not violate local laws. You have to have a clean record, but it is the same NCIC check that is used for all gun purchases now.
The CLEO signature is a problem for some, as some CLEOs see it as "giving permission" or as a cause for a lawsuit if you do bad things with the gun.
If seriously interested, check prices. Manufacture of new Full Autos for civilians was stopped in 1986 and prices have been going up since. Then check state law. If OK there, find a "Class 3" dealer who is licensed to deal in FA weapons (it is a separate class of FFL from a regular firearms dealer).
If you find a seller in your state, and it is legal to do so, you don't need to go through a Class 3 dealer; the seller can get the forms and do the paperwork. This may be an advantage since if the seller sells to a dealer, that is $200. If the dealer then sells to the buyer, that is another $200, plus what ever the dealer charges for the service.
For more info, check the BATF web site.
Jim