BULLSHIT!! Owning an "assault weapon" in the US is against the law. The Brit author has no clue.
You're confusing "assault weapon", a pejorative propaganda term with a constantly changing definition, with "assault rifle".
"Assault rifle" is defined as a selective-fire rifle, chambered for a cartridge of reduced size or power. The definition of "assault rifle" is derived from the German "Sturmgewehr", specifically, the "Sturmgewehr 44", and is a matter of documented, historical fact.
Assault Rifle (Britannica)
"Assault weapons", which refer to semi-auto firearms with certain scary features, such as a pistol grip, or bayonet lug, are perfectly legal in much of the United States (State laws vary).