There are several incorrect or misleading elements of this.

The US standard railroad gauge (distance between the rails) is 4 feet, 8.5 inches. That's an exceedingly odd number.

It's actually not very odd. The distance between the rails is 4'8-1/2". Which sounds odd, until you realize that the width of rail heads is close to 2", so overall the distance between the outside of the rails is round about 5' (though this depends on the rail profile, and it's wider for modern rails generally). So it's not totally a weird number.

Why was that gauge used? Well, because that's the way they built them in England, and English engineers designed the first US railroads.

Neither of those points is completely correct. When railroads began in the US, there were actually several gauges in use in the UK. The UK coalesced around standard gauge by 1850, but there were other gauges in use there. The most prominent example is the broad gauge of 7'1/4" of the Great Western Railway, but there were other lines with other gauges as well, most of which were converted to standard gauge, but some narrow gauge historic lines remain in England. But many British engineers making railways in Britain did not use standard gauge. While it was the gauge of the first modern railroads, it was not so clear early on that would be the case.

The other issue with this is that it assumes British engineers actually used standard gauge when building railroads in other countries. Even within the UK, Ireland uses a broad gauge, 5'3". British engineers also designed railroads in colonies that were 3' gauge, or 3'6", or 5', or 5'3", or 5'6". Many of those networks still remain in the countries where they were built. The advantages of each gauge (smaller, cheaper trains and tracks vs stabilty and greater capacity) were well known, but the advantage of commonality wasn't obvious yet. Even so, even today there's not a whole lot of advantage to keeping a non-standard gauge if you've got a whole network for it already built, which is why the gauge unification has focused on things like getting a single gauge in India (which isn't standard) or figuring out how to allow trains to run on both Standard and Iberian gauge. But countries like Russia and Japan have entire networks already built in non-standard gauges (though Japan's high speed network is standard gauge).

But it's also not true that America always had one gauge. Standard gauge was dominant, but not exclusively. Much of the network in the southern US was 5' gauge. But it was heavily damaged during the Civil War, and with a much better developed rail network and the benefits of a single gauge becoming clear, it was converted in the 1880s. It was sometimes arcimonious, like in the Erie Gauge War, where citizens of Erie PA objected violently to losing their status as the city where gauge changed, forcing passengers to change trains (and thus patronizing local businesses and getting people jobs moving the freight from one train to another). A relic of the gauge anarchy of the 1800s is certain parts of the transit systems in Philadelphia and Pittsburgh using "Pennsylvania Trolley Gauge", 5'2-1/2", which was selected before gauge was standardized.

Why did the English build them like that? Because the first rail lines were built by the same people who built the wagon tramways, and that's the gauge they used.

Early horse-drawn railways did not have any particular fixed gauge, and used a wide variety of them. Horsecar trams actually were built after the beginning of steam railroads, the precedent was mining horse-drawn railways mostly, which were used incidentally by miners also.

Why did the wagons have that particular odd wheel spacing? Well, if they tried to use any other spacing, the wagon wheels would break more often on some of the old, long distance roads in England . You see, that's the spacing of the wheel ruts.

Did wagons really have such an exact spacing of wheels? Before the invention of interchangeable parts I strongly doubt it, but I suppose it is possible. Also, ruts have width, and deep narrow ruts actually will make your wheels get stuck more easily.

And what about the ruts in the roads? Roman war chariots formed the initial ruts, which everyone else had to match or run the risk of destroying their wagon wheels.

An expert in Rome can correct me, but I believe the primary purpose of the roads was for legions marching on foot, not for chariots.

The railroad line from the factory happens to run through a tunnel in the mountains, and the SRBs had to fit through that tunnel. The tunnel is slightly wider than the railroad track, and the railroad track, as you now know, is about as wide as two horses' behinds.

This bit is even more incorrect. Width of tunnels and the like on railroads is called "loading gauge". It is largely, though not entirely, independent of track gauge. A small British underground train and an American double-stack freight train share a track gauge, but have very different loading gauges. Loading gauge varies even more than track gauge, since it is determined by a relatively small number of bridges, tunnels, and wires. It's fairly common in the US to change the loading gauge of a bit of track, usually to accomodate double-stack freight. Western railroads tend to have much larger loading gauges than eastern ones, with inner city commuter tunnels being smallest of all, to say nothing of subways and the like.

As it happens, at over 12' in diameter, SRBs are larger than any of the standard loading gauges in the US (which are themselves wider than two horses), mostly are about how high a train can be before hitting tunnels and bridges, not how wide, so the width of the usual standards is roughly the same. But with the SRBs they were shipped as special oversize freight, which requires careful planning but is not uncommon in the world of rail transport (aircraft components are shipped that way too).