The COVID-19 pandemic brought about an extraordinary rate of scientific papers on the topic that were discussed among the general public, although often in biased or misinformed ways. In this paper, we present a mixed-methods analysis aimed at examining whether public discussions were commensurate with the scientific consensus on several COVID-19 issues. We estimate scientific consensus based on samples of abstracts from preprint servers and compare against the volume of public discussions on Twitter mentioning these papers. We find that anti-consensus posts and users, though overall less numerous than pro-consensus ones, are vastly over-represented on Twitter, thus producing a false consensus effect. This transpires with favorable papers being disproportionately amplified, along with an influx of new anti-consensus user sign-ups. Finally, our content analysis highlights that anti-consensus users misrepresent scientific findings or question scientists' integrity in their efforts to substantiate their claims.