Basic high school physics says this might be right. The larger the wheel,the greater the distance covered with each revolution, meaning more energy needs to be expended for each revolution. Try this on a bicycle where you are the engine and you’ll find yourself working harder with each revolution of the pedals. Since the makers of cars design the drive trains to function with wheels of a specific diameter, it stands to reason that larger wheels will put more stress on drive trains.
Back in high school, I put A/T tires on my pickup. I didn't care about keeping the speedometer accurate, I just had the shop install the largest tires that would fit without rubbing - and the F-100 had *big* wheel wells. The resulting change in final drive ratio made the truck accelerate more slowly. That was with a 3-speed automatic, and the transmission suffered no ill effects. Today's super-complicated eight-speed automatics are probably a different ballgame. I know that you have to have the powertrain control computer tweaked by the dealer service department if you run taller tires - allegedly to keep the speedometer accurate. Who knows, though - it may also change shift points and other stuff.
This image (courtesy of tirerack.com) shows the "plus" sizing common for wheels and tires. I've done up to a "plus two" and not noticed any issues. I think the article is referring to drivers who make much more radical modifications.