On $THH$ and étale base change

We interpret the base-change theorem for $THH$ of Weibel-Geller and McCarthy-Minasian via the description of $THH$ as tensoring with the circle. We thus obtain a simple categorical proof of \'etale descent. However, we give a counterexample to show that base-change fails for faithful Galois extensions of ring spectra in the sense of Rognes.