The first postulate, that the physics of two observers moving at constant velocity relative to each other has to be the same, was already present in the Ancient Law [Newtonian Physics.]
The second postulate is the one that causes what appear to be bizarre consequences, and is "the new stuff." But you must be extremely careful about it, because it is a rigorously precise statement. It doesn't say that objects cannot move with apparent or mathematically implied velocities greater than c [the speed of light in vacuum.] But it does -- as you have correctly surmised -- have that consequence for most situations.
When can it fail? It fails in cases where the motion is not uniform. For example: inside the Schwarzschild radius of a black hole. Spacetime is curved in there, and essentially everything falling into the singularity is freefalling faster than c. Those conditions are, of course, governed by General Relativity, not Special Relativity.
Now everyone wants to look at General Relativity in terms of geometry. That is the lure of its mathematical and conceptual power. But it is also true that the best way to look at Special Relativity is also essentially geometrically.
The real deal on the Special Theory of Relativity is that time and space are not independent of each other. Our universe [where it is "flat", which is where Special Relativity Holds] is not a four dimensional hypercube at all. It is a limited four dimensional surface embedded inside that hypercube, and the limitation is that events that occur on our limited surface which can communicate with each other are required to obey an equation which says [if the event started at time t, then] c2t2≥x2+y2+z2.
[Aside: This is how I get myself into heated arguments with FReepres from time to time who say "someday we are going to break the light barrier." No. We are not. The "light barrier" isn't like the sound barrier. The sound barrier is an arbitrary speed that sound travels in a particular medium. The "light barrier" isn't like that. In order to break it, you would need to actually break the physical geometry of our whole universe. The USS Enterprise's "Warp Drive" doesn't warp the starship. It warps everything. Not. Bloody. Likely.]
OK, now, here are two new assumptions, which are foundational aspects of modern cosmology. They appear to be true everywhere we look and are supported by a lot of experimental evidence. They are the following: 1) The universe, except for random clumpiness [which is interesting for other reasons, but really isn't as important as the guy writing this article thinks it is] is the same in pretty much all directions and 2) It appears to be expanding away in all directions.
If you put those two things together [isotropy of spacetime, and uniform expansion] there is an inescapable conclusion: the further away something is, the faster it will appear to be moving away from you. Steven Weinberg has a very good explanation of this in his book, The First Three Minutes. The best way to understand it is: if you look down the road and the guy in front of you seems to be pulling away from you 5 miles per hour faster than you're driving, and he looks down the road and sees the guy ahead of him pulling away -- also at five miles an hour faster than he's driving -- you cannot really come to any logical conclusion other than that the guy two cars ahead of you is pulling away at TEN miles an hour faster than you're driving. Conclusion: if all points in the universe equally distant are expanding away from each other at uniform speed, and space is the same in all directions, the further away two objects are, the faster they appear to be moving apart.
You can also do this experiment with a balloon covered with dots, which is a nice two-dimensional conceptional model of three dimensional space. [Yes, the balloon is three dimensional, but the increasing radius in that model as the balloon expands is actually t: time.] The expansion of the balloon as you blow it up at a constant rate will have this feature: all equally spaced dots will separate at the same rate, and dots spaced further will be moving faster away from each other than dots close together.
OK... now ... what is the surface of our balloon doing? Objects are not moving away from each other at uniform speeds. The further objects are, the faster they're accelerating away. Therefore ... Special Relativity does notapply! Not uniform motion. Eventually, objects will be so far away that their red-shift will be infinite. The light from them will never reach us, and, they will be receding away from us faster than the speed of light.
Effectively, they are beyond our event horizon. Nothing they do in their own part of the universe can ever reach us, or ever affect us. It's as if they're beyond the event horizon of a Black Hole.
Couple things to note: The objects themselves are not "moving that fast." Within their own little neighborhoods of a couple hundred thousand light years, they think spacetime is still flat and the Special Theory works in empty space very far from strong gravity. But as you look further and further out, it becomes clear that the expansion of space gives rise to nonuniform reference relativity if two objects are widely separated. Second: why doesn't the clumpiness really matter? It doesn't matter because we expect it on the basis of Quantum Mechanics, which we haven't yet talked about. There were random fluctuations in space at just after the instant of creation. Those fluctuations were incredibly small -- smaller even than the size of an atomic nucleus. But multiply those fluctuations of energy [which eventually became mass, then stars, and galaxies] by how fast the universe was moving and how long it's been moving, and next thing you know, you see a background of stars at large distances that doesn't appear to be uniform. And it isn't. But that doesn't really change the uniformity and isotropy of spacetime a whole lot. And it doesn't change the Hubble Law.
That's what's going on here, and what this author doesn't understand.
[Aside: There is actually a decent explanation of what happens in the other direction, as you look backward in time to the Big Bang, and what happens to past events here:http://roger.blogs.exetel.com.au/index.php?/archives/186-My-Future-Light-Cone.html If you've followed what I've said here, you should have no trouble with it. ]
Sorry for an overlong explanation. Sometimes I miss teaching physics...