Sure they did....."Perfect Sound Forever" was the specific claim and slogan that they went by.
Also.......my records have extremely low levels of pops because I take proper care of them and have a cleaning machine that I use religiously.
As for the differences......I have had probably a couple of dozen people of varying backgrounds from 15 year old kids to good studio players and every single one of them could hear the difference and I'd guess 90% of the time they prefered the vinyl. And they couldn't just tell the difference because of clicks......on my clean records there basically are none. But there is a discontinuity to digital that 16bit/44.1k sampling isn't enough to hide and it affects the sound.
To me a good example of this is amp modelers like the POD. I have all the main modelers...a POD, a J-Station and a V-Amp and although they are wonderfully fun tools, there is a lack of 'snap' to them that I just can't stand. Now lots and lots of guitarists think they're great with no flaws........but I clearly hear the difference and it's not simply because of pleasing 2nd order distortion. It's because a digital recording is a series of steps rather than a continuous curve and also, the time delays, as small as they are, of converting A/D....doing the processing and then D/A conversion. I don't care how fast it does it...it still takes some amount of time to do all that and that, I think, 'causes the loss of instant response or 'snap' that I hear.
NOTE: I am not claiming to hear a delay in the digital stuff, I'm just saying that it alters the transient response and thus, the sound.
Also....16bit/44.1 cuts off reverb tails which makes things not sound quite right even if you don't know why.
I have three nice stand-alone audio CD-burners and I can always hear a slight loss of .....I don't really know how to describe it, but a slight loss of something when I record a LP.