but only if their binary is linked against a gpl library..?

Nope, it is enough to distribute any binary made with GPL source code to have an obligation to publish the code. As soon as you use GPL code, no matter if you modify it or not, you have to re-distribute the source code you used.

"The source code you used" which you obtained from GPL sources.

You do not have to distribute proprietary source code which has not been incorporated into the GPL code (the definition of this varies depending on whether the GPL code is GPL, LGPL, etc.)

They're shipping Linux. There's certainly plenty of GPL binaries in their system.