The Tripp-lite video linked by the O.P is pure unadulterated bullsh!t and marketing w@nk! Apart from a stack of multi-socket adapters that would make a fire-marshal wince, the 0.5V 'limit' for ground noise comes from near-obsolete bipolar TTL logic thresholds and has nothing whatsoever to do with noise voltages measured between Neutral and Ground at the wall outlet, which may (or may not) accurately represent common mode noise.
Basically TTL logic chips were built of bipolar transistors, and couldn't pull a logic '0' output right down to 0V due to the low side output transistor's Vce_sat. This was about 0.3V, maybe a bit lower in ideal circumstances. The specified logic '0' input threshold was 0.8V, below which any signal was guaranteed to be seen as a '0'. The actual threshold at which the gate switched would be a bit higher, between the specified logic '0' and logic '1' thresholds, but you couldn't count on the extra margin. Subtract 0.3V from 0.8V and you get 0.5V, which is the maximum amplitude 'ground bounce' that could be tolerated at the Gnd (0V) pin of a TTL chip with respect to the Gnd pin of any other chip it was connected to. This is all low voltage 5V DC stuff, nothing whatsoever to do with the power coming from the wall. There certainly wouldn't be a connection from Neutral to the logic board. Also, PSUs don't (and never did) contain TTL logic connected between Neutral and Ground on the input side!
The demo in itself is rather suspicious. Its obvious something is filtering out the 60Hz power-line fundamental frequency from the Tripp-lite 'engineer's scope display. There shouldn't be very much of it on the Neutral to Ground trace, but I would expect some signs of it. On the raw Line to Ground signal, there is a whopping great 117V RMS, 331V pk-pk 60Hz sine wave, probably with distorted peaks ('flat-topping') due to other loads in the building and neighborhood consisting of SMPSUs without good power factor correction, with the line noise riding on top of it. Obviously that's undesirable when you are trying to measure low amplitude noise on top of it as most scopes wont have the resolution to resolve small signals riding on one several orders of magnitude larger. Filtering or cancelling out the fundamental frequency to a sufficient degree to be able to directly measure noise at the tens of mV level would be extremely challenging. You've got to attenuate it by over five orders of magnitude without significantly attenuating the noise you are trying to measure. This would be possible if the mains supply was a fixed frequency pure sine wave, but it drifts slightly with the load on the grid, with up to +/-0.05Hz variation being entirely normal and excursions up to about +/-0.1Hz not unusual. This makes it impractical to use a high Q notch filter to reduce the fundamental by sufficient orders of magnitude (as you'd have to keep tweaking its tuning to follow the line frequency to get adequate rejection), so either the 'magic box' measurement interface is filtering out *ALL* low frequency signals including low frequency noise, or its doing some very complicated DSP to track the fundamental frequency and its odd harmonics (from the 'flat-topping') and actively cancel them. In practice, its commonest to simply high pass filter the power line signal and effectively ignore all noise below the filter cut-off frequency.
If I was a suspicious sort, I'd not want to bet that the 'magic box' wasn't entirely rigged, maybe with a high bit rate audio player loaded with tracks of various sorts of noise, controlled remotely by someone off-camera.
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