This guy is simply pulling numbers out of his ass. Using the standard NH M gear profile in simc we have this scenario:
First of all, we see that the ring compared to no legendary at all is roughly a 6.2% increase, but compared to another 940 legendary (sephuz in this case) its only a 4% increase.
With the ring we see 17.7 fury spent per second and with sephuz we se 15.6, which is roughly 13% more fury.
For those wondering, yes the sim is using meta when its up and syncing it with chaos blade in the shoulder build (it has on average 130 seconds cd, 126 with shoulders+ring).
Here is a comparison for 2 legendaries combined, we see the difference still being below 10%
So if you'd like to reroll for the chance of getting 4% additional damage then all power to you, but farming +15 m+ is gonna net you more overall damage than rerolling for the time spent.