I think there is a lot more here than is being covered.
Looking at the manufacturer's site there is a lot of information, and a lot of it actually makes sense. However the sale of these devices for domestic use is not something that makes any sense. As Amir notes, a balanced mains feed does not meet code in the US for domestic use. The manufacturer has an FAQ that quotes the code, and is quite clear about this. However, their web site has two parts, one for commercial use, where this FAQ can be found, and a domestic side for AV applications, where nothing is mentioned about domestic use being a violation.
So, what is the device's real use case, and is it reasonable?
The device is sold for use in professional sound recording applications, and its use case is simple. It entire job is to help manage grounding issues. No claim is made about magic clean power. Everything is directed at building an installation where common grounding problems can be eliminated. This isn't a trivial installation, and is well beyond any domestic application. Amir's tests exactly match what is expected of the device. No snake-oil or woo. But in domestic settings the device has no role, and marketing it into one is both a violation of safety codes, and won't do anything that the device is intended to help.
The entire idea is to allow the creation of an isolated power run that is referenced to a "technical ground". Basically this is a new proper ground that bonds the system ground to a new externally created ground (you get to drive rods into the earth) that is otherwise separate to ground that the rest of the building's power is bonded to. After that, everything connected to the balanced power is grounded to the technical ground via the ground connections on the supply. Cheater plugs are thrown away if they were in use, and all the usual correct grounding and balanced signal reticulation rules are used. The result is supposed to be a system where all the noise problems inherent in recording studio systems (and these can be a serious mess) can be eliminated, and a proper safe system created.
The supply includes its own GFCI, which is of course balanced relative to the technical ground. So, in principle, the entire system is safe.
So why is the device built as it is?
Interestingly they claim very high quality steel is used for the core. Which is odd. Usually you do that to improve frequency response. Which with a power isolation device is generally what you don’t want. Indeed Amir’s results show this. However the rationale seems to be that they don't want the transformer core to introduce distortions of the waveform itself. They trumpet a bifilar wound secondary the ensure avoidance of asymmetric waveform distortion. The device is designed from the outset not to filter external noise. So Amir's measurements actually confirm the manufacturer's design goals. This isn't a filter, and should not be judged as one.
The manufacturer's products do see use in professional recording and other professional audio applications. But not as a line filter, because it isn't one. Its entire job is to help manage grounding. The manufacturer's FAQ provides a detailed and pretty reasonable sounding set of how-tos to help debug and cure noise issues in a recording studio. In the end all the claimed sonic benefits come down to managing grounding and noise issues that result from them. No doubt, in a recording studio, with distributed sets of equipment all coupled together, grounding issues and noise is a very real problem.
Sold into domestic settings is much more problematic. Code requires that these devices are only used in properly supervised environments where there is a need for a technical ground. So clearly for a domestic setting these devices should not be used and they should not be sold into them. Without a proper technical ground installation they won't even work as designed to help with grounding.