A good example of how sensitive everything in the Standard Model is to everything else is a
recent post by Jester on rare Kaon decay measurements (the most recent of which match the Standard Model with some modest tension). The branching fraction of this rare but otherwise unexceptional decay is sensitive to 1 PeV BSM particles. And, this isn't an outlier. The "every possible path contributes" aspect of quantum physics and SM physics calculations means that a significant deviation almost anywhere propagates almost everywhere. So, if we aren't seeing problems with SM predictions almost everywhere (and in fact, we see just the opposite, consistency almost everywhere), this is pretty strong proof the the whole edifice is sound and complete.
So, why propose a Hidden Valley if would have so minute an observable impact on anything?