The code of the service has multiple copyright holders. Some published code under the GPL, others didn't publish the code at all. If the service code were to be published, it could only be published under the terms of the GPL license.
However, it is the right of each copyright holder to decide whether their code shall be published. If the code were to become public against their will, that would be copyright infringement. The right to control whether a creative work is published is more fundamental than the GPL. Therefore, the illegally published code would not have a valid GPL license attached to it.
The GPL FAQ has a related entry:
If someone steals a CD containing a version of a GPL-covered program, does the GPL give the thief the right to redistribute that version?
[…] If the version in question is unpublished and considered by a company to be its trade secret, then publishing it may be a violation of trade secret law, depending on other circumstances.
I think that the FSF's reference to trade secrets is correct but not necessary, and that the illegal publication is already prevented by copyright law. So what the thief is doing is illegal whether or not they are stealing from a company that has trade secrets.
Jurisdiction-specific arguments for the US (but this is going to be similar anywhere):
Distributing copies of a copyrighted work is the exclusive right of the copyright holder(s) under 17 USC 106. A thief has not received permission from the copyright holders of the service, therefore the thief is performing copyright infringement (17 USC 501(a)). The GPL restricts the service's copyright holders that they must license the code under the GPL if they distribute it, but does not compel them to distribute it in the first place.
Possible counterargument: if the service is a joint work then all joint authors might have full rights to the work. A joint author cannot “steal” their own work by publishing it. However, a lot here would depend on the specifics.
If the service was created as a work for hire, the developers are not copyright holders and have no rights in the software. Joint authorship cannot apply in that case, and this would be plain copyright infringement.