No. Not really.
A 3D printer can make a gun. So far the ones produced have been oversized single-shot pistols but we can expect that to improve.
The article is fearing nanotechnology. Instead of using a specific kind of plastic or metal to make its products like current 3D printers, a nanotech assembler can mix and match atoms to make whatever design it's been handed. That could include weapons of mass destruction. There are biological experimenters who could make a lethal plague without using nanotech. With nanotech chemical weapons, explosives, and gnat-sized killer robots become possible.
But not nuclear weapons.
3D printers and nanotech assemblers are just building things from the inputs they're given. They can't break or combine atoms to make new ones. Carbon in, carbon out. Creating your own atoms would be picotechnology, and nobody's forecasting that yet.
An A-bomb needs fissile material. Uranium and plutonium are preferred. You're not going to find that at the local hardware store when you buy feedstock for your 3D printer. You can't even settle for any uranium or plutonium atoms--it has to be the right isotope. There are people with the full time job of noticing when someone goes looking for that stuff.
H-bombs also need an A-bomb as their trigger. On top of that they need deuterium and tritium. Sure, you could try extracting that out of your own water supply, but it'd take a long time and be noticable.
So don't be afraid of the neighborhood hacker making nukes. He can make lots of other WMDs, but not nukes. So be afraid of him for that. Be afraid of political science professors who don't know enough to realize when they're making public fools of themselves. And be afraid of editors who don't know how to fact-check technology articles. Politicians listen to them.