Then, the second paragraph begins "In lieu of using replication slots... use keep_wal_segments"
This is talking about using keep_wal_segments to always have certain minimum number of WALs even if replication is up-to-date and doesn't need those WALs anymore.
Also, if the slot is managing the storage of WAL segments, then isn't there a possibility of filling up a disk in the event of an outage?
Yes, which is why you should have disk alerts set in place and a quick way to redirect WAL files to another machine, possibly one that stores backups.
And would keep_wal_segments prevent that?
No. If slave is out, slots will keep all WALs irrespective of what the wal_keep_segments is set to. So in a way, wal_keep_segments value is the lowest minimum number of WALs you will have on master at any moment, and with slots it is possible that number will increase if slave goes down.