"solid mass of copper "
Not really - is full of holes for thru holes, SMD pads, vias, traces, etc. If you use eagle and look at the actual top & bottom layer you will see it is not very solid at all. But it does cover the top & bottom layer where nothing else is.
Congratulations, you have earned the title of "Which Tyler" - Leader of the Pedant's Revolt.
Compared to traces it's a "solid mass of copper". In the same way that I am a "solid mass of blubber" - yes, there are bones and organs in there, but the majority of it is blubber.
Oh, and the vias and through holes join different sections of the ground plane together using... guess what ...? Copper. The ground plane, despite being a convoluted shape with other things going through it is, despite what you may thing, a single solid entity with no breaks in it. Yes, it goes around other things, but it is unbroken. If it weren't then it wouldn't be much of a ground plane now would it? It would be 17 ground planes with nothing connecting them :P