Bruno Putzeys has mentioned that while using a star ground will work at low frequencies, it can give rise to noise problems at higher (RF) frequencies. So if we are talking DACs (or anything with some processor noise) or Class D amplifiers, using a star ground scheme may not be the best idea.
Generally, I consider Mr. Putzeys to be a pretty accomplished engineer. He has mentioned that the star ground will have too much impedance for high frequency noise, hence the recommendation to connect pin 1 direct to chassis with the shortest possible wire, right at the input point.
This is an interesting distinction to me, as I am sure a well implemented star ground will eliminate typical audible hum problems, I find that there can be more subtle sonic degradation caused by RF noise issues, and eliminating these lesser effects is of great interest to me, especially in the world of contemporary components where there are all kinds of sources of RF pollution.