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From the BRB FAQ p. 8:
Q: Do modifiers that apply to such things as Reserve rolls, apply to
units from an allied detachment? (p124)
A: No.

So if I have an allied Psyker with Divination and get Scrier's Gaze, can I roll three dice for the Reserves of my primary detachment? In other words is it a modifier? Or is that a moot point as it doesn't specifically say the Psyker makes the Reserve roll?

From BRB p. 420
Scrier's Gaze is a blessing that targets the Psyker. Whilst the
power is in effect, you can roll three dice and choose the
result you want when rolling for Reserves, Outflank and
mysterious terrain.

Doesn't the FAQ you quoted answer your question? If I understand you, it seems that it does... But maybe I just don't really understand your question?

The FAQ says that modifiers from a primary don't impact an allied force. It doesn't seem to apply as it references modifiers.

Modifiers are things that will increase, decrease or set the target characteristic or roll. In this case, you aren't modifying the roll or target number needed; instead you just get to roll 3 dice and pick which one you like.

I'd say that RAW, you can do this.

I would say it works, although I did manage to roll 2 1's and a 2 for it yesterday :(

Ah yeah, I didn't pick up on the 3 dice part... Yeah rolling a 3rd die is not a modifier so the FAQ doesn't apply...