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if you gained access to a discipline through the Martial Training feats, then you will have a non-standard initiating stat.
Also archtypes for core classes that grant initiator abilities. And multiclassing (which is much more effective as you gain 1/2 of other class levels). Lastly, school/discipline swapping.
The long answer is, they learned from Paizo's mistakes and didn't publish abilities with hard coded stat dependencies. You can search the forums for posts about spells that state they use the "normal" classes attribute despite the caster's class using a different attribute. There is an FAQ stating that they don't get to use their class attribute making the spell far worse (as they typically don't have that stat) despite it being a "class spell".
PoW's wording prevents possible issues like that by just stating to use the class that grants the ability's stated attribute. You can have multiple initiator attributes via multiclassing, just like you can have multiple casting stats (wizard/cleric multiclassing for example).
@OP: There are numerous reasons to word it like that and they have nothing at all to do with "changing the initiator attribute".