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I don't see why? They could be indistinguishable from our perspective while mysteriously being affected in some way if certain things happened to their "partner". We can experimentally set an upper bound on the permissible weirdness but I don't think we can eliminate the possibility.

Experimentally you'd be attempting to detect inexplicable single particle events above some level of rarity. You'd have access to only one side of the pair - you can't tell which one the other side is even if it's right in front of you (and it almost certainly isn't). So there's no discernible (to you) trigger for these events you're trying to detect. So you'd be trying to correlate frequency counts with bulk conditions as averaged across more or less the entire universe.

In the same vein as the God of the gaps the phenomenon could always be hiding below the noise floor.