I think it is lacking in the documentation, but you should make this call using the page access token instead of the user access token in order for it to work.
So here are the steps:
Get the following permissions from the user and get user access_token
:
manage_pages
- to get the page access tokenread_insights
- read readings (as indicated in the document)read_stream
- for all messages that the current session user can view
Using this token, get page access_token
with a call
/{page-id}?fields=access_token
(optional) Check my answer here to extend the access token on this page, expiration never . (Basically, to avoid some steps)
Using the page access token, run your request -
SELECT post_id, actor_id, message, impressions FROM stream WHERE actor_id = {owned_page} and source_id = {owned_page}
This will display the results (if any) in the results.

Hope this helps.!
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