I don't know about the rest of Europe, but in England and the French lands in the High Medieval period a wealthy landowner needed his feudal overlord's permission for a castle to be considered authorized. An unauthorized castle would certainly be considered a statement of some measure of independence from said feudal lord. Building a castle was an expression of power being exerted over territory; therefore a nobleman who built without his lord's permission was implicitly defying that authority. Whether or not it was actually a sign of open rebellion, or simply a side effect of a weak central authority, certainly changed from case to case. Depending on the politics at the moment, maybe the overlord could do something about it, maybe not. For example, the Dukes of Normandy in the 10th and 11th centuries were frequently able to do as they pleased, considering the relative weakness of the King of France at the time. In the 12th century, the English monarch held the right to approve all new castle construction; during the conflict between Stephen and Matilda for the throne of England, there were a large number of so-called "adulterine castles", referring to fortifications built by local lords without any royal approval during the national anarchy.

Anyone who owned their own house could fortify it by building a fence or wall around their property, and - if it was a particularly wealthy family who owned it - could man said wall with their tenants.

Do you have a particular place or style of fortification in mind?

Depending on the type of fortification, keep in mind, these were typically extremely expensive. I'm talking hundreds of millions, if not billions in today's currency for a castle or large keep. This would pretty much put out everyone but government and wealthy land owners.