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Ironically, in statistics, and in the application of statistics to science, a significant result is one that is measurably different from zero. So when a scientist says "no significant effect" they don't mean "there is an effect, but not a significant one" they mean "there is no measurable effect".
That STILL doesn't mean it's zero, like you said. But it does mean that if the effect was actually zero the data would still be the same. That's because rabies data is famously unreliable. Often by the time they're diagnosed, victims are nonverbal. We can get an idea of the species where the stain originated from, but that doesn't mean that's the animal that bit the person. If a bat bit a cat who bit a human the test would turn up bat. So was it a undetected bat bite, or a bat infection in a non-bat carrier? We'll never know because the patient can't explain anymore. Is it zero, is it a small amount? We don't know. But what we do know is that if there is a connection between undetected bat bites and rabies in humans, that connection is weak enough to be undetectable using the data we have.