If you want to nitpick, I can point out that the full quote is "Europeans between about 500 and 1300 mostly couldn't paint"; stress on "about", and those aren't paintings.
Besides the comment started by saying that "medieval European art generally sucked", so it covers the work I mention.
That's if you want to nitpick. If you don't, both those works are hallmarks of medieval art and while they're not necessarily exemplars, it is important to remember that there were still artists who knew their stuff in and out in medieval times and the Renaissance didn't come out of nowhere.
Edit: I travel through Europe by train a lot (mainly France and Italy but also Switzerland and Germany occasionally) and I visit museums, cathedrals, and art galleries in every city I stay. I have seen a lot of medieval art because those places just seem to have it lying around by the bucketload. There is a broad range in quality, but I have seen some very high quality woodcuts and, indeed, paintings, although those tend to be religious icons. Sculptures also, but mainly in statues of saints on the outside of cathedrals (see e.g. the Rouen cathedral). I'm trying to say that I'm not some kind of art authority or expert on medieval art, but I have seen my fair share of it, and no, Europeans didn't just suck at art in the medieval. I think what happened is there was a lot of mostly religious art that was lower quality, sort of like you can find plenty of slop on the internet today, but there were still skilled artists that created shockingly good art. You'd be more likely to find it in the palaces of the rich and powerful, I reckon, because they were the ones who could afford/support talented artists, as opposed to more ordinary craftsmen, who would be paid less. For the same reason you might find less of the good art lying around than the rougher, cruder kind, because the former was more expensive and thus harder to obtain. This also goes for religious art, which tended to include a smorgasboard of art forms, from painted icons and sculptures to reliquaries and liturgical equipment like communion chalices. But good medieval art existed, I've seen it, and it wasn't that rare.
It's not nitpicking. 1450 is not between 500 and 1300. You may stress "about" but I certainly didn't.
I put the cut-off at 1300 very intentionally. As soon as you go much past 1300, you start to see stuff like this https://en.wikipedia.org/wiki/Andrei_Rublev#/media/File:Rubl... That's some good shit. I see this in Wikipedia dated 1338: https://en.wikipedia.org/wiki/File:Lorenzetti_amb.effect2.jp... Not bad at all. They're already creeping up on or El Greco or Da Vinci or something.
And if we move the cut-off all the way to 1450, fuhgeddaboudit. You have freaking Albrecht D\:urer by that time. No fair. I'm sorry. The challenge concerned a particular 800-year period, which I chose carefully.
Yes I hear you about the range of quality. You're right. Many of the best pieces may have been "exhibited to death." There was presumably lots of student art and whatnot, probably not considered very good at the time, but it happened to survive. I accept that. But I'm only asking for a single counterexample in an 800-year block of time. I think that's fair.
If you like, though, I'm happy to amend my claim to this: "No, medieval European art did not suck. European art between 500 and 1300 sucked. But from 1300 until whenever the Renaissance starts, watch out. Those folks did some really nice work."
Well then that's not nitpicking, it's cherry-picking, trying to fit your claim into a specific but arbitrary period. You start by saying "medieval European art", then you reduce that to "between about 500 and 1300". Why between 500 and 1300 specifically? What happened to the other ~200 years?
It doesn't matter. There was plenty of good art between 500 and 1300 too. I mentioned the Rouen cathedral, whose west front, the one with all the statues of saints and the hyper-detailed architecture wikipedia tells me was "first built in the 12th century, entirely redone in the 13th century, and then totally redone again at the end of the 14th century, each time become more lavishly decorated" (https://en.wikipedia.org/wiki/Rouen_Cathedral#West_front). That's just one example that fits your spec, that I have personally visited. As I say I'm no expert.
Here's another: the sixth-century basilica of San Vitale in Ravenna, Italy, with some of the most famous mosaics ever, including those depicting emperor Justinian, his wife, empress Theodora, and his court, which again Wikipedia tells me were completed in 547.
With a cursory look online I can also find a bunch of other famous art pieces from your chosen period that I haven't seen myself, like e.g.the Diptych of the Virgin and Child Enthroned and the Crucifixion (https://www.artic.edu/artworks/16241/diptych-of-the-virgin-a...) which however is very typical of the ecclesiastical art I've seen in many museums and art galleries I've visited.
So I do think your claim is a bit exaggerated, even if you try to limit the time period carefully. There was always good art made in Europe.
Btw, I'm Greek so I'm not offended by your claim about Europeans, in case there was a lingering doubt about that. The Greek middle ages (i.e. Byzantium) are usually not included in the European middle ages but Byzantium produced absolutely gobsmacking art throughout the medieval so leaving it out is also a bit arbitrary (but that's not your fault).