Nowhere in the article does it mention how much larger the balls are. Microns? Millimeters? Inches? The balls could very well be within spec, as I suspect, and someone is out for some free advertising.
You'd think they could collect some of these balls and test them.
The CORE size would not necessarily alter the size of the ball. They would just wrap it tighter. As long as the weight and outer size are within specs, no one would know. There was a report on TV where the balls being made in Central America were being wound too tight.
As far as size, the American League has a slightly smaller specification than the National League ball, or at least they did years ago.