Typically not. Usually companies lease the right of way (power lines, conduits between manholes, etc) on extremely long terms and pay to install the fiber / copper themselves. Cities that "own" the fiber directly are what would be considered "municipally owned."

Cities may also provide "franchises" so that only one telco or cable operator gets the right to lay cable pathways, and all other companies are denied the rights. This is usually coupled with the company picking up the cost for actually building and maintaining the rights-of-way (ie, actually building the manholes/conduits, or whatever). There's thousands of cities, and many hundreds (if not thousands) of companies in the game, so its expected that there are many different variations between each municipal area.