Saying that the FBI infiltrated Anonymous is like saying that they’ve infiltrated antifa; it’s a category error.
For most of its existence, 420chan has been plagued with administration incompetence and downtime, so I find it very hard to believe someone who can't even run a site is secretly masterful at hacking them.
That is almost the definition of the "hacker group Anonymous". It / They are a swarm of swarms of undefined individuals who join these various swarms based on their own ideologies, motivations, availability, skills, and current level of life boredom.
This is it's greatest strength: if it hits "viral internet meme" popularity, it can actually achieve a productive level of coordination / chaos with no specific 'head' that can be cut off.
It's also it's greatest weakness: As you've described, the ability to (mis)attribute blame, ie. "state cyberattack disguised as ..." because there is no cohesive group to need the reputation points of claiming responsibility.