There was always a Royal Navy presence on the convict ships, even if the ships were privately hired. Why? Well, apart from the possibility you mentioned (which

There was always a Royal Navy presence on the convict ships, even if the ships were privately hired. Why? Well, apart from the possibility you mentioned (which is unlikely -- just you try committing piracy on British soil in the 19th Century in a ship with its name and identifying information written on the back), there was presumably the possibility that a captain might let a prisoner escape in exchange for money. Also there's the problem of maintaining security on the prisons. And finally, I'm sure there was a constant need to cycle guards as well as prisoners back and forth from Britain to the colonies.