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.
"It says he made us all to be just like him. So if we're dumb, then god is dumb, and maybe even a little ugly on the side." -- Frank Zappa