I'm not sure I understand this response -- basically all of cosmology involves theories based only on somewhat subjective interpretations of sensor data targeting far-off objects. So I don't necessarily disagree.
But what could possibly happen other than they act like all other physical objects do? It boggles the mind to think how broken physics would have to be to accommodate a second correspondence principle for the big-but-not-too-big scale...
I feel like maybe I'm misunderstanding your sentiment, because this seems like a basic shared fact: a clock anywhere in the universe is still a clock.