Quote Originally Posted by Me, the incredibly smart and beautiful RITA MORDIO
Had I counter claimed immediately, I would have risked death, and then if I had survived I would have risked being killed that night. After all, the mafia would know that I'm not mafia, so they would know that I'm town rather than an independent, and I'd be a nice easy target whenever it was convenient for them to kill me.
I feel like I should clarify this part. Reading it back there's a logical step that I haven't explained.

One of the factors that made me want to hold off on counter-claiming straight away was the possible presence of the Cop. I can't remember if we'd confirmed a cop at the point Raven made his claim or if it were merely a possibility. Anyway, if you suspect a cop is in play you basically confirm that you aren't an independent. I pointed this fact out myself when Raven made his claim:

So either Raven is telling the truth or he's mafia. We can pretty much rule out him being the Lyncher or the Survivor at this point, as if a cop investigated him and he showed up as 'other' instead of mafia then he'd be signing his own death warrant.
Basically, when there's a cop in play you only claim miller when you know you're going to investigate as 'mafia'. Which means claiming Miller with a cop around makes you either town or mafia. From a town perspective... you could be lying. So that makes you 50% mafia or 50% town. Mafia, however, know that you aren't mafia. Which makes you 100% town, and reduces the risk that they'll waste a night kill on an independent.