He’s just taking the scaling of the Gamma variates outside of the Gamma distribution, that’s fine. I think this is something computational rather than mathematical. All those R-hat values are 1 so this is from a single chain.
@aaronjg Did you see if the traces take excursions like when you try to sample directly from the student’s t without reparameterizing? Did you look at the N_eff/iteration for more chains (e.g.-10)?
I’m not dismissing what you are seeing, I think there could be some real cautions we should be pointing out about re-parameterizing scale parameters.