I think the discussion is in danger of wandering off into a philosphical dead-end. So in an effort to try and stay more in touch with the scientific method and away from philosophy, let's use an operational approach to what we might actually measure via a thought experiment.
Suppose we have a gravitational wave interacting with two, free floating test masses in an inertial frame. The actual situation on the Earth is/was more complicated, we'll avoid the complications of how we compensate for the Earth not being an inertial frame, and instead focus on an easier to analyze idealized experiment carried out far away from any perturbing masses.
So, we've got two free-floating test masses (and because they're test masses, we assume that their gravity is negligible), and two rulers. One ruler is based on the current SI standard, another ruler is based on the old platinum bar standard.
For more details, see for instance
http://www.nist.gov/pml/wmd/metric/length.cfm
The definition of the meter (m), which is the international unit of length, was once defined by a physical artifact - two marks inscribes on a bar of platinum-iridium. Today, the meter (m) is
defined in terms of constant of nature: the length of the path traveled by the light in vacuum during a time interval of 1/299, 792, 458 of a second.
What happens when the gravity wave passes?
The free-floating masses move as measured by the both rulers so that the distance between the test masses as measured by both sorts of ruler varies. The amount of movement is essentially the same within experimental accuracy, as one might expect the "new" standard based on the light standard behaves almost identically to the old standard based on the platinum bar.
I said "almost the same". Why not exactly the same? The short answer is that neither the light-based ruler or the platinum bar ruler is perfectly rigid, but it turns out that the platinum bar based ruler is less rigid than the light based ruler, and we can operationally view the passage of the gravity wave as exerting a perturbing tidal force on both the test masses AND the rulers.
The theoretical notion of "perfectly rigid" that I'm using to judge both rulers is called "Born Rigidity". This may be of some interest, but it would be too much of a digression to go off on a tangent and explain any more details than this.
The important thing to realize is that the two test masses are moving relative to either sort of ruler, and that within experimental error (certainly parts per thousand, probably parts per million) the two results agree.
Let me add that there is absolutely nothing wrong with viewing the gravity wave as a metric pertubation, and that's in fact how it's reported by the Ligo group. The question becomes as to what the physical significance and interpretation of this metric pertubation is, and the answer I'm suggesting to this question of physical sigificance is that one looks at the Riemann curvature tensor , which in lay terms can be regarded as being equivalent to the hopefully familiar notion of a tidal force, or tidal gravity.