[Q]

Phoenix-D there a both abilities available and both are used in the fate shrine.
From the ability file:

Change Bad Intelligence Chance - System
Value1 = Percentage change in chance for bad intel event for entire system (+/- percentage).
Value2 =

and

Change Bad Event Chance - System
Value1 = Percentage change in chance for bad event for entire system (+/- percentage).
Value2 =

It is however very difficult to test if the bad event chance works and I never did that.
However the intel change did not work when I tested it some time ago.