In a word, yes - LPs vary quite a bit in sound quality. Even different instances of the same pressing. I collected audiophile LPs for about 20 years. I had individually numbered small-batch white-label promotional pressings without liner notes, pressed on 200 gram vinyl, Japanese press, half-speed masters, 180-220 gram heavy vinyl, 45 RPM single sided, Audioquests, Cheskys, BMGs, MoFis, vintage RCA Victors, you name it. Most I bought in new / unplayed condition from dealers at HiFi shows, others were used in mint condition. I cleaned them with a Nitty Gritty 2.5 FI and played them on a high quality rig; Thorens turntable, Ortofon MC-30 Super II, with a DACT CT-100 phono amp powered by dual 12 V batteries, properly aligned and tuned, sitting on the floating wooden lid of a 200 # sandbox for vibration isolation. So I felt that I was hearing about as close to what the vinyl sounded like as one can get, with as little coloration as possible. I've posted an audio clip or two from them here you can find if you search.
A few were really special, like the MoFi 200 gram Muddy Waters Folk Singer. Or a limited issue half-speed 200 gram pressing of Dizzy Gillespie's Big 4 from Fantasy. A white-label promotional Telefunken of Ludwig Streicher playing bass-piano duets, half-speed on 200 gram vinyl. And some of the Audioquests had fantastic sound.
Different pressings were different like night & day, not even close. For some of the LPs, I had several versions of the same pressing. These were closer in sound quality, but still different enough to very easily tell them apart. Overall, the variance in sound quality with LPs is quite wide, or conversely put, the quality control quite poor.
All that said, the site you mention seems overkill to me. But that's just my opinion. It's a free country and one man's trash is another man's treasure. When I sold all that vinyl on eBay, I was happy to discover people willing to pay several hundred bucks for a single record, if it were something special and pristine. I certainly wasn't cheating them out of anything. They were 100% happy customers. There definitely is a difference in sound. How much it matters is every person's opinion.
All that said, you're better off buying something that is tangibly different, like a half-speed master on heavy vinyl or Japanese press edition -- compared to a "hot stamper" which might be the same plain old record that some random guy thinks sounds better than the other 3 in the rack.