If you come across a FileMaker Pro client being able to see a FileMaker Server, but not being able to see hosted files, you might need to replace the server.pem file on the Filemaker client application.  The issue stems from SSL connections to Filemaker Server.  

You can remedy the issue by replacing the server.pem SSL certificate file on the Problematic install of FileMaker Pro with one from a working system. 

FileMaker Pro Server.pem files are found;
Windows: 
Server.pem file found: Program Files > FileMaker > FileMaker <ver>  (copy Server.pem)

Mac OSX:
Server.pem file found: Applications > FileMaker <ver> > FileMaker <ver>.app > Contents > MacOS” directory.  (copy Server.pem)

Move the working Server.pem file from a working installation of FileMaker pro to FileMaker installation with the problem and replace it.  (located as above)

More Info from FM Forums:  (lengthy posting discussions)

more Info @ FM Forums