I'm not positive but I would assume that a second earth rod on a subpanel even when bonded to the main earth rod does not remove the requirement of the subpanel to be grounded back to the main panel. The object is to prevent any current from being generated on internal wires when lightning strikes one ground system, but not the other. The different potentials create a huge current surge which will burn everything on the way. Profuse grounding conducts the lightning voltage everywhere so no current can flow. In theory... Of course houses still burn down which are properly grounded because lightning is not predictable.
Speaking of lightning, a good friend of mine, some of you know him as Lensman from AC, has a great theory about temporary electrical connections that I'd like to share since he hasn't found his way over here yet.
Microsurface peaks and valleys in the metal conductors prevent a perfect mating surface through which current can flow. Between the adjacent peaks that actually conduct by contact, there are millions of peaks that nearly touch but have a small air gap. When voltage potential builds between the two "mating" contacts current flows through the touching peaks with increased resistance which affects current flow, which is one way sound is affected compared to soldered joint. The resistance at these contact peaks also alows potential to exist at the non-contacting peaks with small gaps. Lensman's theory is that the tiny air gaps between adjacent non touching peaks are small enough to permit arcing even at small micro-voltages created by the high resistance contact point at the touching peaks. The arcing generates RF and all kinds of nasty effects that ruin the signal as it is passed through the temporary connection.
This is why the contact enhancement products work, even those which are not conductive per se, like Torumat and Cardas, they fill the gaps with a stronger dielectric than air and reduce the arcing. Maybe this is why Walker SST, which has silver particles in it to increase the number of contact points, is made with canola oil instead of petroleum grease, canola is a better dialectric. This aspect must be significant a advantage because polyunsaturated oils will harden over time like good oil paint. Petroleum as dielectric must be less effective than plant based oils. Vaseline is 2.6, same as castor oil at 80F, castor oil is used in audiophile oil caps. Linseed oil 3.1 (>60%unsaturated), cotton seed oil 3.1, Mineral oil used in industrial transformers is 2.1, Olive oil 3.1, crude petroleum oil is 2.1. Hydrogenated oils are much better dielectrics and would not oxidize (Crisco!), but they are too solid and would prevent contact. Partially hydrogenated castor oil might just be the ultimate contact enhancer with dielectric around 5-6! But it is disgustingly messy, sticky and stinky.
Olive oil is a monounsaturated fat which has identical dielectric strength as canola without the tendency to dry or oxidize. Should make a fine contact treatment! And door hinge lube!