Police reports are always a good idea, but hardly the only method of proving damages did or did not exist. You'd be surprised how many cops cannot see damages that do exist after an accident.
The fact is that you did hit the ambulance, and likely jarred the people inside, even at a low speed. Logic dictates that there is going to be some damage, even if it's minimal.
Even at low speeds, a rear end collision can cause injuries that may not show up for a few days. This is not unheard of. For an insurance company faced with this possibility, it's a lot better to be safe than sorry, and to treat the initial injuries rather than waiting for them to become really serious, or to wait to be sued for not paying what they legally owe in this instance. Insurance companies don't just pay claimants if there's no proof of injury. And if you think every insurance company out there doesn't operate like that, then you're kidding yourself. People who change insurance companies because they don't understand the process and are angry that they're being held responsible for an accident and injuries they or a driver they gave permission to drive caused amuse me to no end.