I recently heard it claimed that objectivity in science requires direct
Your specific argument in terms of X, Y, A, B, C doesn't quite work. I don't know what it means to say that "the value of Y correlates with directly measureable variables A, B, C"
I think that your overall point is fine. Our measurement of many scientific quantities e.g. Avogadro's number, Planck's constant is indirect, and calculated from direct measurements. That does not mean that these measurements are infallible--both direct and indirect measurements can be erroneous.
It is also worth worrying a bit about what is meant by a "direct" measurement: does it have to be something we can see unaided, or can it be something we can "see" or "detect" through an instrument? There may be no important distinction between direct and indirect measurement.