I can see why some companies are not on board with MQA, which of no reason stated really have to do with quality, more to do with fees and control.
My understanding after reading Wiki, lossy is used a lot but it refers to the method used to reduce the file size. Here's a statement I zoned in on, " it hierarchically compresses the relatively little energy in the higher frequency bands into data streams that are embedded in the lower frequency bands using proprietary dithering techniques but after the decoding the result would be the lossless archive"
I'm sure methods are different but the same type of thing is done with DTS-MA or Dolby's Tru-HD. The master is compressed to safe space but once decoded is said to be the same as the master. I don't remember their methods ever being questioned as to the decoded file resulting in nothing less.
So, yes, the article calls MQA lossy, I wonder if correctly so, but the end result that we playback looks to be lossless.
The reason I think lossy is not correctly applied, they actually mention mp3. In mp3 information is actually eliminated, we can't decode or restore an mp3. Some try to make it sound better but lost info is just gone. With MQA the original file is just folded if you will, nothing is lost. Then unfolded to it's original state again.
From a purist's point of view I can see how no manipulation would seem better than some. On the other hand the uncompressed original file would take considerably more bandwidth and could theoretically sound worse if your internet or other gear wasn't up to handling it.
That's my take on it as of now. This is first I've given this issue much attention so I'm open to learn.
Wikipedia does a better job than I can of explaining it.
Master Quality Authenticated - Wikipedia