Shannon's limit is a Mathematical principle.
Unfortunately, most people have next to no understanding of mathematics beyond some rote memorization from school. This is just another example of people confusing analog signals with magic. To be fair, the actual researchers involved probably understand this quite well, but the scientifically uneducated class from which science and technology journalists are drawn is another matter.
The non-mathematical version, for those interested, is that yes, analog signals are continuous and so can occupy an infinite number of states. The reason you can't get infinite bandwidth out of that is because both the transmitters and receivers have limited precision, and because there is always noise, which is another manifestation of the Second Law. For example, there are an infinite number of real numbers between 0 and 1. If you could actually use all of that space, you could encode any amount of information in an arbitrarily short signal. (Well, there's a limit to that, too, for which see Georg Cantor.) In practice, you can't use all of that space, because your instruments might distinguish quite well between 0.001 and 0.002, but they can't reliably tell the difference between 0.001 and 0.0005. On top of that, there is noise, which is also a big topic, but you can think of it as a random fluctuation in the signal. If the ambient noise varies between 0.0 and 0.0005 in the same example, you can't even reliably tell the difference between 0.001 and 0.002.
What the parent is getting at is that laws of physics, being derived from observations of nature with limited precision, might occasionally be overturned by better observations. Fundamental mathematical principles, on the other hand, are much more reliable. There might be a difference between rest mass and inertial mass that we could exploit for thrustless propulsion. It's extremely unlikely, but it can't be ruled out. But there is zero possibility that 2 + 2 will ever equal anything other than four. Shannon's limit and, for that matter, the Nyquist sampling theorem are a little more complex than a simple integer sum, but the actual math for both would fit on an index card with plenty of room to spare to blather on about "infinite" analog signals. We use digital signals most of the time these days because it makes the hardware easier to design, but neither digital nor analog can be used to make an end run around the Second Law.
What the researchers in TFA claim to have figured out is another way to use part of the signal outside of the frequency domain to stuff data into. It's a really ingenious approach that might be quite useful if it pans out in actual practice, but it's not magic, and it's not infinite.