Am I overlooking or is there something really wrong here?
First, all files of a tablespace should be inside PG_9.3_201306121 directory, why do you have those other files? Second, there shouldn't be any hard link inside of a tablespace, as PostgreSQL is not creating them, someone must have done it by hand. I'm guessing all inside PG_9.3_201306121 is linked to the root path of the tablespace, which is wrong.
If I'm not overlooking, then neither barman nor pg_basebackup is to blame, but whoever created the hard links; if PostgreSQL did this (which I doubt) then it is a bug.
Might it be hardlinks created by pg_upgrade? If so, they can just be removed...