The issue eventually resolved itself.
I found that Graph API Explorer allows to choose attachments edge while constructing feed query that in this case appears like this
https://graph.facebook.com/v2.1/me?fields=feed{attachments}but execution of such request triggers "Unsupported get request" exception.
It seems like non-working attachment edge for feed was unimplemented feature or a bug, because, surprisingly, now all attachments are retrieved successfully as subattachments collection.
Thanks, everybody.