1. They are using high end analog gear clipping for saturation.
So?
You can get better sounding clipping with analogue gear mostly, but that's not what we're talking about.
2. Generally you are listening to the mp3 which generate intersample peaks, the lossless audio probably doesn't clip.
Intersample peaks are there before. Mp3 conversion can generate clipping from it but also maybe not. Could also generate.
Lossless audio has intersample peaks too.
3. The mix sounds like crap and squashed lacking dynamics.
Only if you've squashed your mix. A mix doesn't have to be smooshed to have intersample peaks. Like I said plenty commercial well produced records with peak values greater than 0dB
Intersample peaks are largely about the playback device...
Yeah mp3 can create clipping by trying to assume and reconstruct the peak.
But what happens with intersample peaks is that thay *TRUE* PEAK value is higher than "0dBFS" so when your audio plays back, it's actually playing back with louder peaks than you realise it has... this can cause distortion in the playback device if it can't handle those values.