Since the secondary side of a transformer is a new service there must be a grounded conductor. Since there is no XO from the primary the secondary must be corner grounded. In other words one of the secondary phases
Not true...there is no requirement for a 480 volt delta system to be grounded.
In other words one of the secondary phases (it doesn't matter which one but H3 is cutomary) must be bonded to the EGC. This phase will then read 0 volts to ground while the others will read 277 volts and voltage phase to phase will be 480.
Also not true. The grounded phase will read "0" volts to ground, the other two phases will be 480 volts to ground, and the phase to phase voltage will be 480 for all combinations.