This is just an intuition but I think in hierarchical models, hyperparameters (\tau, \mu) might not need to be as strictly checked as parameters (\theta). Hyperparameters being well recovered would be the necessary conditions for a good parameter recovery and propositions such as all parameters passing SBC test would guarantee good results for hyperparameters could be made.
So if your aim is to test the overall model, not how well a specific hyperparameter is recovered, it might be economical to test parameters only.
I wonder what other SBC people might think about this!