From the engineering viewpoint, (I am not an electronics engineer but how I see it), the data comes in as bits, those 1's and 0's you see the robots using as sentences above. Think of those as no more then instructions, like a manual on how to put together a Lego pirate ship. If one of the bits was wrong, you would not be able to build the pirate ship. So when these instructions come in, the chip decodes the information and turns it into soundwave signal and that leaves your DAC on to the preamp/amp. The reason we were making fun of that is because if data got corrupted, you would not be able to rebuild the sound wave, just like your computer monitor would be sputtering different colors, the images from Pluto would have all kinds of anomalies etc. Data being fed to a DAC is no different, it is just data, sentences, instructions on how to rebuild something. If the data is getting corrupted it would be because the source device is sending it wrong, not because the receiving device is corrupted it.
As far as why the DACS sounded different, make sure they are precisely level matched to within .5db or better. This type of precision is hard to achieve by a novice. I would bet if in your tests your group got the levels matched under .5db or better and could magically change the signal from one DAC to another without delay, you would not even know that a change happened. But yea, the level matching needs to be identical for you to not hear a difference.
Lastly, just because something cost $100k+ does not mean it sounds better. It is pure marketing, the only place IMO that this type of expenditure could be warranted is on speakers. For electronics, its just not that complicated. Think about your computer CPU, mine has IDK like 16 cores and can do billions of calculations a second, it only cost me $500. My point being, Wadax is an expensive DAC claiming to solve made up issues that do not even exist. They are not inventors or genius scientists, they are nothing but salesman taking money from the rich.
You have to remember that a lot of the people I see talk on here are actual engineers. These guys went to school and learned, IMO, some hard shit to learn, I struggled through basic circuits class myself. I think you should put more weight into what they say, then the company trying to separate you from $200k+ for phony claims. Do those Wadax guys even have EE degrees? I doubt it, they would be to ashamed of themselves to make false claims.
Speakers are where the differences are IMO. Electronics, we have that licked. Just think about what today's CPU's can do next time someone tries to tell you you need to buy a $200k+ DAC because it fixes the Lego Manual instructions that were sent wrong by the source. Oh and while the CPU is doing billions of calcs a second, it makes no errors, probably like .0000000000000000000001 percent chance of an error idk. So decoding a FLAC is childs play.