Is there any evidence, stated by Blizzard or others, that the cooldown of Spirit Vessel is reduced whenever Grave Injustice is triggered?
No, Spirit Vessel is not affected by the cooldown reduction of Grave Injustice.
Which is a little counter intuitive, as the text on Grave Injustice would indicate that all abilities have their cooldowns reduced:
Whenever an enemy dies within 8 yards, regain 2% of your maximum Life and Mana and the cooldown on all of your abilities is reduced by 1 second. This range is extended by items that increase your gold pickup radius.
Fundamentally though, the cheat-death effect of Spirit Vessel is more of a proc than a cooldown. This is backed up in the many build discussions around the use of these abilities together, including this quote:
It does not sadly. Would be an absolutely amazing, and quite overpowered, change if it were to ever happen.
While Grave Injustice does not reduce the cooldown for the cheat-death proc, it will stack with the cooldown reduction for abilities such as Spirit Walk.