Thank you for this thread, I landed on it after mulling over this very same issue for some time. I just wanted to add the location of the switch mentioned here for anyone else that may be experiencing this issue. The switch for excluding the private files was on by default and a bit buried. You can find it in your Search API index settings. As of this writing it was under [your index name]->Processors->[Processor settings area]->File attachments[tab on left]->Exclude private files switch should be at the bottom.
The order I used that worked on the first try was:
Ensured that the "Preserve cached extractions across cache clears" switch was off in Search API attachments settings
[don't forget to submit]
Flipped the "Exclude private files" switch in the index processor settings off (again don't forget to save - you should get a message that everything is scheduled for re-indexing) if you don't, click the button to reschedule everything in your index before reindexing.
Go to index and index now
Now finally rebuild your Drupal Cache so that it will appear in your search results.
Turn "Preserve cached extractions across cache clears" switch back on as desired...
This may differ depending on your Drupal Configuration but I hope it may help anyone else landing here.