Question

Can your own Pokémon disobey you in Legends: Arceus?

Comments

Yes. Source: experience

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Definitely possible, because the Star system from the Galaxy Team explicitly tells you what level of Pokemon will obey you.  Though, I haven't seen it happen.  But then again, it's been ~3 generations since I've had a Pokemon disobey me despite being a fair bit above the given badge level.

Answer 1

Yes, it depends on your Survey Corps Rank Level.

Star rank 1: Pokémon level 20 or below will obey you
Star rank 2: Pokémon level 30 or below will obey you
Star rank 3: Pokémon level 40 or below will obey you
Star rank 4: Pokémon level 50 or below will obey you
Star rank 5: Pokémon level 65 or below will obey you
Star rank 6: Pokémon level 80 or below will obey you
Star rank 7: all Pokémon will obey you
(source)

The higher the Pokemon's level compared to your Survey Corps Rank, the greater the chance it will disobey. (E.g. if you are star rank 1 and have a level 21 Pokemon, it's much less likely to disobey you than a level 60 Pokémon.)

Answer 2

Yes, even if you successfully catch them, if they are a higher level than the Galaxy Team rank level cap that you are at, they have a chance to disobey.
Source: Caught a lvl 65 alpha Ninetales at rank 4, it refused to attack consistently until I got to the next rank.

Comments

I've never had this problem, my team has been always obeyed me no matter how many stars I've had. Maybe it has to do with how many you levels you are over the cap?

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This only affects caught or traded Pokemon over the level cap. Pokemon you raised yourself are fine.

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I never traded in LA but my level 25 beautifly wouldn’t obey me at rank one. I can confirm this is correct