I'm assuming you paid by credit card, but that your card issuer doesn't offer rental insurance... And that you didn't take the optional insurance offered to you by the rental company.
Yes, secondary, and correct.
My credit card does have insurance, but I'm pretty sure it's secondary. I'd just assume not deal with them yet. My normal auto insurance covers rentals, with a $500 collision deductible (versus the $1500 of damage, according to Hertz).
I called my own insurance (Amica) and was speaking to a human agent within minutes. They said I can file a claim with them, pay my deductible, and they'd conduct an investigation, giving me back my deductible if/when they determined that I wasn't at fault. Alternately, they said I could file a claim directly with the other guy's insurance (Allstate). I just called them and they said it was a 46 minute wait queue. I'm going for lunch, then I'll give them a shot later today.
*sigh*