You know, that comic has always bugged me a bit. The quantum electrodynamics bit makes sense, but I see no way all that GPS devices are dependent on relativity to work. To get them to work right, we have to design them to account for the predictions of relativity, rather than just classical mechanics, but if the universe ran on classical mechanics rather than relativity, I can't see any way in which it would prevent us from creating GPS devices; it seems to me that it would be even easier.

Relativity has loads of experimental support, but unless you count nuclear energy, which was already observed before the advent of the theory of relativity, if not explained, then I'm stuffed for examples on how industry's benefited from it being true.