Or just user error, though that could fall into a technical reading of "guest evaded taking one at all".

I know someone who just got a positive PCR test and still got two negatives on at-home test kits.

I think you mean false positives? Or are they just bad all-round?

Relatively high yes, but with emphasis on the relatively; I would be surprised that there would have been more than 3 false negatives.

And only the one person returning from South Africa would have needed to actually be a false negative. The rest may have been true negatives.

At least in my social and work circles, it's pretty normal to take a test before attending a larger gathering, or meeting more vulnerable people.

But then, Denmark has an average of 17 tests per person, the highest in the world by some margin.

Norway is 1.6 per person, Finland 1.5 and Sweden 1.4.

Based on what evidence you making that statement. For myself living in Sweden I can say that almost everyone does a self test when they have even the slightest of symptoms. Also I would argue of all places in the world, Scandinavia is probably the place where one would find the lowest propability of lying about a test.