It's more complicated than that. The DB as an umbrella organization (consisting of over 100 companies) is publicly owned, but:

• The infrastructure is completely separated from operations, with a lot of regulations to make sure that the infrastructure company doesn't cooperate with any operations company for fear they might discriminate against other companies, effectively throwing sand into the gears of railroad operations because many communication paths that are standard in other railroads are banned.

• The companies that carry out operations are expected to be completely self-sufficient, with no direct support from the government, but only through contracts auctioned off to the lowest bidder for local services (definitely no connection with competing companies who bid really low regularly going bankrupt /s). Long distance services are expected to finance themselves but are expected to cross subsidize services to cities that aren't quite as lucrative (because they are, after all, owned by the government) and at the same time compete with companies that aren't government owned that just offer rides on the most lucrative routes.

• The budget that is available for infrastructure is decided by the government every year, meaning absolutely no financial stability. This means that construction companies don't end up growing because it could be too risky, and when suddenly there's a lot of work to be done the few construction companies that are able to do the work demand insane prices and conditions, and the infrastructure company is essentially forced to swallow if they want anything done at all.

Source: I work in this clusterfuck.