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I think it depends on whether they really did throw the firebomb.
If they're the firebomber, it sounds like classic Confess to a Lesser Crime, since the idea is that confessing to the lesser crime makes it seem like they've cooperated and have been honest, as opposed to denying the whole thing despite at least some evidence to the contrary. For example, if there is strong evidence he threw the brick and weak evidence he threw the firebomb, it's a tactical admission.
If they're not the firebomber, it might be part of a Plea Bargain to just admit to the misdeed (plead guilty) and get it over with. This can be smart if there's no chance of being found Not Guilty in court. From the police's perspective, maybe this character is a Red Herring for having means, motive, opportunity, but nope, they really didn't kill anyone.
A person is suspected of throwing a brick into a recruitment center, followed byba firebomb which burned the place and killed a baby. He admits, repeatedly, that he threw in "a brick and nothing but a brick".