I have a paper, that I can insert as reference in Google docs. But when I review my paperpile.com it does not exist/show up.
There are no filters set, and I look in “all papers”. I have one folder which is shared with another person, whom are working together with me on the project.
It sounds like you or your colleague may have added the paper to the document. If you added it, it would still be available in the document even if you deleted it from your library because we do not want documents to break when people make changes to their library.
You can add papers in a document to your library by going to Paperpile --> View all references, in the Google Docs menu. Each of the references added by others will have a button for adding it to your library. You can also use the hamburger menu at the top to add all papers.