Independence of administration Art. 2. No public authority, including the Riksdag, or decision-making body of any local authority, may determine how an administrative authority shall decide in a particular case relating to the exercise of public authority vis-à-vis an individual or a local authority, or relating to the application of law.
https://www.riksdagen.se/globalassets/07.-dokument--lagar/th...
And the problem for that 1 person was that Tegnell dismissed asymptomatic transmission. Dismissing the possibility of asymptomatic transmission led to making a mockery of his plans.
Everything since then has been an attempt to save face, including coming up with nonsensical excuses about how Sweden cannot do some things because “free dumb” (which it has since proceeded to do anyways).
Ironically, the faceless bureaucratic nature of public health in most countries allowed them to change tacks when they were wrong. In Sweden, since Tegnell became so intimately connected with and responsible for the Swedish response (to the point that politicians would blindly accept what he was saying), it became difficult for him to accept where he was wrong and then change strategy accordingly.
The rest of the world had it easier. Politicians would blame the WHO and China, public health officials would anonymously blame the politicians, and vice versa.
Within all this blaming it was still possible, as various public agencies in the rest of the world have, to actually change and improve responses based on new information since no one individual was tied to the earlier plan.
Of course, in general, the Swedish system is a lot better. But the pandemic has exposed a flaw that it’s over reliant on a single source of expertise. They mah need to consider having a separate private source of expertise (for example, the UK has something called SAGE) that can step in if the original source is unable to make necessary adjustments.
Also, it's even more complicated since FHM don't have authority to tell other government institutions how to run their business. You could call them a governmental support function, if that helps.
Regarding that Swedish politicians are "free dumb" and "they can't do anything". We have laws that could impose lockdown in the event of war, but these laws do not apply to a pandemic/epidemic. My understanding is that Norway and Denmark have similar laws, just that they do apply to pandemics/epidemics. I don't think it is right for politicians to have the ability to lock up people when the law does not support it. We should have had a law that could be used during a pandemic but we didn't.
I also think that the asymptomatic carrier thing is more complex than you describe. I don't think a majority of the cases were from asymptomatic carriers and if you follow the recommendations (social distancing + wash your hands etc.) it wouldn't be a problem.