You are using the Brady campaign to defend a weapon's issue?
back to the point.
The image shown with Palin holding a weapon is a simulator. The weapon simulated is an M4. You can spend all day calling it a vibrator if you wish, no one in the military will agree with you.
The key to the definition of Machine Gun in the military comes down to crew served weapons. A Machine Gun is a crew served weapon. Even the M249, The Squad Automatic Weapon, is not called a Machine Gun, just as the BAR, Browning Automatic Weapon, was not called one.
The M249 is issued to an individual, not a crew. A M240 is a crew served weapon. The M2, The Browning .50 cal Heavy Machine Gun is a crew served weapon.
You could attempt to call the M4 a sub-machine gun, but then again, the definitions do not back your statement.
A SMG uses a pistol cartridge, rather than a rifle cartridge.
BUT- from your own arguement:
An automatic weapon (machine gun) will continue to fire as long as the trigger is depressed (or until the ammunition magazine is emptied).
The M4 fires from semi-automatic to three round burst. It will not continue to fire as long as the tigger is depressed, and so fails to fall under your own arguement.