I'm not really following the subtitle you have, but the answer is yes - governments did use private naval forces. They were called Privateers, and were by and large, pirates, but with an official licence to raid and plunder the ships of other nations.

So, how did it all work? And why did it happen?

The major factor was the colonization of the Americas. The Spanish Empire was most powerful during the period immediately following the acquisition of the Central and South American colonies. The wealth that the Spanish were shipping out of South America was attractive to all of the European nations, naturally, and this led to many pirates, merchants, and other members of society sailing across the Atlantic to chase fortunes that could be made through capture of Spanish ships.

The Spanish colonies weren't well defended, and were often abandon by their inhabitants when ships were seen. The fleets transporting wealth back to Spain were protected by armed ships sailing with them.

Most of this was going on during periods of war. However, when Elizabeth I died, England and Spain made peace. Piratical endeavours against the Spanish were not allowed anymore, as they breached the peace. One example of this is Sir Walter Raleigh, executed for raiding a Spanish outpost in modern Venezuela. He had been a favourite under Elizabeth, not so under James, her successor.

To get around this ban on piracy against Spanish ships, the men who ran these ships that preyed on Spanish merchants applied for letters of marque. These letters were used in peace and war, but for different purposes. During periods of truce, they were "an instrument of private redress," where governments provided citizens "who had received injury at the hands of foreigners" with legal right to get compensation from other subjects of that state. In simpler turns, if you lost a ship to a Spanish pirate, you could get a letter of marque giving you the permission of the English crown to raid Spanish ships for compensation. In other words, it was legally sanctioned piracy, and the holders of these letters were known as Privateers.

However, the New World was not a place of peace, and the workings of letters of marque were different in wartime to peace. Despite no official war, the French, Dutch, Portugese and English frequently passed out letters of marque, making almost anyone who requested one a sanctioned pirate. The common target of these privateers was the Spanish, and as such, anyone caught privateering was treated the same as a pirate - death by hanging.

This punishment was common, because although they were legally sanctioned by their own governments, the Spanish had accepted no such sanction, and viewed them all as pirates. The authorising papers these ships carried were only useful in that they protected them from neutral parties, and allowed them to sell their ships in port. Anyone who captured a Spanish ship and attempted to sell it through an English port without the proper papers could be arrested as a pirate - only the papers gave you legal permission to sell a captured ship.

P.S. sorry I took so long to reply, I saved the thread and forgot about it with work.