Said another way, LIGO can't work because the ruler itself is squashing as space squashes, so you can't measure if space is compressing.
I think the chief confusion here is that you may be thinking the light arrives at the detector in the same amount of time regardless of spacetime curvature. That is, the the ruler is itself squishing.
But what needs to be considered is the constant speed of light.
This implies that what happens is, in the presence of additional curvature, and constant speed of light, the additional distance traveled will have appeared to slow the light.
In the laser interferometer this registers as interference.
https://m.youtube.com/watch?v=ajZojAwfEbs
It is also worth noting that any claims of detection are thoroughly investigated and confirmed with other detectors.
It is difficult for a single LIGO detector to confirm a gravitational wave signal on its own. The initial discovery of gravitational waves required that the signal be seen in both detectors (Hanford and Livingston).