History is littered with stories of people who thought they anonymised data and later discovered something they did not think of. The only surefire method is not collecting. That doesn't mean there aren't better ways to do it than others, of course.

Accident locations are a public record, police reports are a public record, so you can't keep those away from those with the carrier database.

Of course, another thing I didn't point out is that the carriers do not want solid evidence that talking on cell phones, even with a headset, is dangerous!