Last year I joined a support group on Facebook for people who believed they were suffering from long COVID.

I was shocked at the sheer number of people who believed they had COVID between December 2019 and April 2020.

Presumably they're mostly Americans? That's a big range of time, and having Covid in December 2019 is somewhat unlikely but the chances were not zero (Wuhan is a big city with direct flights to international destinations, including New York and San Francisco), if an American told me they got Covid in April 2020, I would believe them, because the government was keeping that number officially zero through bureaucracy ("You didn't travel to China, we won't test you!" and later "Hey, we've found zero Covid cases!"). There were probably also a number of Americans (or Europeans who soon after travelled to the US) who partied in Ischgl, the Austrian ski resort which became a super-spreader site during the months of February and March.

https://abcnews.go.com/Health/disaster-motion-flights-corona...

And Google Trends for "fever": https://venturebeat.com/2020/09/02/google-releases-data-set-... , but well, it was winter, a comparison of Winter 2019 and 2020 would've been useful.

some degree of false positives and negatives would be expected, but "no relationship" is still shocking

Not really? Most covid cases are mild, and the symptoms cross over with those caused by a lot of other pathogens. For people who didn't get tested and have mild symptoms, there's no particular reason to assume they had covid, but given the fact that (especially earlier in the pandemic) they are constantly reading about it, people are probably predisposed to assume it's covid.