New Reanimator rule question (EoD)

So, the reanimator rule got changed (for the better, I think) to read “For each Friendly Core Skeleton unit within 6”, you may re-roll one dice that failed to hit with Drain Life, Fireball, Heal, Hex, Surge, Weakness, and Wind Blast, to a maximum of 2 re-rolls.” (it’s up on easyarmy already).

However, I noticed that it says “each” and not “each other”, and Cursed High Priests already have the Skeleton rule. Am I missing something from the “core” keyword, or do they automatically give themselves 1 reroll?

Additionally, Balefire Catapults have the Skeleton keyword as well, and if they count, it could be a nice little “battlegroup”, especially if you can surge it to keep up with the priest during the first few rounds.

No, pretty much every rule/aura that effects the unit itself explicitly states that (inspiring, radiance of life etc).

Catapults work, as do other high priests