first they make claims about timing, not about absolute resolution or fidelity. because that indeed wouldn't stand. now for timing, the basic simple trick is using higher sample rate. as they then compare the MQA 48khz container to a 48khz PCM, magic, they have better timing information as in the container they have 96khz sample rate. it's a trick and at the same time it isn't.
another aspect they claim to improve and they do, is that they reduce ringing at the band limiting frequency nobody really cares about but them. they do that by keeping high sample rate and by going for what I imagine to be a mix of filters the same way many moderns DACs do. they then want to play that game at the ADC, while selecting the output format and filter type of albums to be released, and at the DAC. the end result is that, congrats the ringing is almost gone and they can show a Dirac pulse for everybody to misinterpret how it looks, for fidelity. :/ of course his comes at a price. for a general idea only, you can think of using only an analog EQ to low pass. when you mess with FR you also change phase, and vice versa. here the entire philosophy of MQA is "we go all in for the time domain!". bit depth, boom pay the price. frequency response, boom pay the price. but they aren't lying about that, they really take great care of one out of 2 variables to define the signal.
as for file size, and lossy, yes the format is in some ways lossy as soon as they apply dither or go for some lossy compression of the ultrasonic data as they seem to have the choice to do. but the file size of a 24/192 isn't evidence of it. because no MQA content will ever be 24/192. once extracted it will be more like 18/192 maybe, maybe less. so right there you save a good deal of space. lower resolution does that ^_^.