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This is why the laser is split, and sent down two perpendicular paths. Sure, a wave might stretch the spacetime of the X axis... but that same stretching wouldn't effect a similar increase in the return time of the Y axis. This very stretching of the measuring device itself against one axis(thus modifying the round-trip time of the split laser as compared to a perpendicular path) is the very thing that they are measuring.
Your pet theory, and their experiment, match.