That's correct English. I tried it as well and it was marked wrong, so I've reported it.
Sitting "on" a chair and "in" a chair are both grammatically correct and should both be accepted. They are a bit different in connotation: one might sit "on" a hard wooden chair, but "in" an upholstered armchair. Also, sitting is not ordinarily reflexive in English. "He sat himself down" (never "he has sat himself down") would imply a deliberate act, perhaps balancing on an unsteady chair for instance, or making a formal entrance, as in "the Chairman came in and sat himself at the head of the table."
'He sat on the stool' was incorrect, but Stuhl should translate to both chair and stool?
Auf den Stuhl...why is 'onto the chair' nit accepted? Auf den clearly indicates movement 'onto'
But wouldn't it have to be dative to involve movement? Den Stuhl isn't dative, in that case it would be Dem Stuhl right?
It's the other way around. Akkusativ is for movement and Dativ for position/standing still. So when somebody sits on the chair, he is moving (he isn't already seated). Hope I helped.
Ah, yes, I really don't know how I mixed those up. You indeed helped, have a lingot!
So I guess the most plausible answer to the originally posed question is that; in English we never use the word onto along side the action to sit regardless of movement.... At least I've never heard it that way.
So we have to use the reflexive form here? Will "Er hat auf den Stuhl gesetzt" be marked wrong?
I don't seem to understand when I should use 'sich' and when demonstrative pronoun like mich, dich, etc. Edit: I found a link with a table of reflexive pronouns: https://www.lsa.umich.edu/german/hmr/Grammatik/Reflexiv/Reflexiv.html#Table