only what can be done this way is someone from this "Everyone" group to read,modify or damage Avast! Data folder files ... in that case he can maximally read logs or cause Avast! to not operate correctly ...
there are no executables nor loaded libs so infection with trojans not come to place ...
YET another problem could be ability of "Everyone" to place file there and then execute (full control right)
- but that would mean anywhere in filesystem on actual PC is "Everyone" set to READ ONLY right... ie schools like someone mentioned
in such case Avast! DATA folder rights could turn into 'issue`
possible solution for future, while installing / updating avast! there should be dialog asking about directory access rights allowing to choose Everyone or Custom ... or st like that ...
i'm i missing something