In How to Construct Multicast Cryptosystems Provably Secure Against Adaptive Chosen Ciphertext Attack, the paper states under preliminaries:

We consider the scenario where a single party, called the center, sends messages, over insecure channels, to a group U of n parties who are denoted members of the group. In such a setting, the center often has a special role. Since it is often distributing information of its own choice, it is assumed to have control over the group membership, i.e., the center is allowed to make decisions about who can join the group and whose membership should be revoked. This is in line with almost all multicast schemes such as [25, 4, 26, 27, 22, 23, 24].

We assume a computationally bounded adversary who is allowed to attack the system from both outside and inside the group. The insider’s attack is modelled by allowing the adversary to corrupt and gain total control of up to t group members where t is a predefined threshold. We only consider non-adaptive adversary who chooses what members to corrupt before the key generation.

Since the center U authorized the inside attacker, it seems disingenuous to claim that an inside attacker can ultimately access the message.

What is the significance of inside attacker or threat? Why should we care about it in this case?

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The "significance of inside attacker or threat" is making the problem non-trivial.
We "should we care about it in this case" because the
protocol apparently claims to provide some sort of revocation.

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