S3/Cloudfont files not really protected?

Perhaps I’m not quite understanding how this is supposed to work, but I have several PDF downloads in an Amazon S3 bucket; I believe I have these set up correctly to be available only to members of my site. However, if I click on the link to show these PDFs when I’m logged into my site, S2member then creates the huge URL, but if I copy that and paste it into a browser on another computer from which I’m not logged on, I can access that file from there. In other words, anyone can copy and paste the URL S2member generates to access protected files on my S3 bucket, and then anyone, member or not, appears to be able to access it just by pasting that URL into a browser. I’m obviously missing something, but can’t figure out what it is!