To be honest, I disagree with that claim, and would suggest that the author is unreasonably overstating his case.
Balanced connections have certain advantages, especially when it comes to immunity to noise, and especially with long cables.
This is the reason they are much preferred for pro audio equipment (where long cables and noisy environments are the norm).
However, in most consumer applications, and in situations where equipment is relatively close together, or the environment isn't especially noise, those advantages simply don't matter.
(That's why a balanced connection is great insurance against noise issues if you're running long wires, or running wires through walls, where they may run near power lines or light fixtures.)
It's also worth noting that, until recently, most consumer audio gear didn't have balanced inputs or outputs.
Therefore, if we hadn't standardized on the now-ubiquitous RCA connector, we would have standardized on a different unbalanced connector instead.
The top candidate there would probably have been the BNC connector...
BNC connectors have more secure internal connections...
BNC connectors actually lock to BNC panel jacks - so they cannot pull out or fall out accidentally (the locking mechanism on BNC connectors is even more secure than the one on XLR connectors).
BNC connectors have been the connector of choice for high-end test equipment like oscilloscopes for decades.
(The main reason why RCA connectors won out over BNC connectors was the cost - BNC connectors used to be far more expensive.)
(Back when RCA connectors came into common use, the XLR connectors used in balanced connections were also quite expensive, which is the main reason why RCA connectors won out.)
It is worth noting, however, that the circuitry associated with balanced and unbalanced connections is somewhat different.
Therefore, with any specific piece of gear, the actual internal circuitry is either balanced or unbalanced.
And, if you connect either type of gear using the other type of connection, your signal must pass through a simple circuit to convert it.
(It is almost certain that differences in this conversion circuitry account for any audible differences between the two that you might hear other than noise issues.)
RCA connections are "still being used after so many decades" because they perform quite adequately for the job at hand.
(And modern RCA connectors are significantly more well designed than the originals - which usually weren't even gold-plated to avoid corrosion.)
The author makes this statement in the comment section under the review.
Not only does this make sense technically, I've consistently heard a difference myself.
