That sentence is entirely true for the GUI.
calibre, due to its linux heritage, has a pretty complete CLI backend which can replicate most/all of the GUI functionality.
As such, the server can be started on its own via a CLI executable, which naturally enough stays alive as long as that CLI executable process is running -- which is to say, it is decoupled from the library GUI.
re: your bugreport, the sentence in Preferences is not actually wrong, nor does it contradict what I said.
That being said, if you are saying it should be enhanced to notify users that the CLI
alternative allows you to close calibre and leave the server running, I guess I can hear that (although I don't know how many people would actually be willing to do so and therefore benefit from the doc change -- most prospective CLI users already know
).