Obviously not true. Else how can people in the service job hopped around different agencies? You always see the peak during May - Jun and Aug - Sep period where people resign/second/transfer to join new agencies.

Word of caution. If you do apply for jobs (within the Public Service) while still in current place (also within Public Service), it is possible that they will contact the HR of your current place. And naturally, the HR will contact your boss. Especially true if you've went through the interviews and they are considering you. Not always, but may happen. So it may be polite to tell your current boss you are considering elsewhere.