I haven’t heard that. The teachers at my friends children’s schools were home if they were ill. I think the general guidelines were to stay home at any sign of illness (so the also caught less common symptoms of the coronavirus). I believe Sweden was relying on lack of evidence for high transmission from children to adults (but I may be mistaken).
There are so many factors. Sweden did many things wrong as well, they failed to protect the elderly in homes. There was a lack of safety information in foreign languages, which may have impacted, guidelines were based on the typical Swede (lives alone or core family, extremely compliant with regulations etc) and migrant areas where families lived together in generations were disproportionately hit.
I think holding the schools open up to year 9 was a decision they were very happy with. I even believe the wishes they have extended it up in age groups a bit, but I may be wrong.