The field "from" returns nothing in this query:
https://graph.facebook.com/v3.2/(page id)?fields=posts{comments{message,created_time,from}}&access_token=(page access token)
The other fields return what I expect. I'm administrator of the page but I haven't submitted my app for review because according to this page I don't have too, or am I wrong?
From the page:
Does not require App Review.
Grants your app access to the default fields of the User object that are a subset of a person's public profile:
id first_name last_name middle_name name name_format picture short_name
Or is there anything else I could have done wrong?
Without authorization, you cannot get any user specific data anymore, no matter if you own the Page in question. You can only get data like the message or the link to facebook.com.