IMNHO "File server" implies it exports an actual file-system, and would also be wrong. In that light, I think S3 is more like FTP than a "file server". Sure, it might technically be more like WebDAV than FTP, perhaps "FTP-like service using HTTP for transport" is more accurate -- but I'm not sure it's better than just calling it FTP...
Well, yes, they aren't OOP objects. But as you say, "files" isn't great either. But it was a theoretical alternative. For example, you could do a search/replace on the S3 docs here: http://docs.aws.amazon.com/AmazonS3/latest/dev/UsingObjects...., and they would still make sense.
But FTP isn't even close. You could not find/replace "Object" with "FTP" without making those docs completely incoherent.
That's the wrong comparison though. You could replace all instances of "S3" with "an FTP server" and it would make a ton of sense, minus the reliability claims.
"S3 - Simple Storage Service" describes pretty well what the point of the service is without making strong claims around what it may or may not be. It's a service for storing things; it's not a database or a filesystem. The devil is in the details of course but even when I was really new to cloud services I got the gist of what S3 was supposed to do.