Nothing is wrong with the statistics, it's how you use them. It's just difficult to meaningfully say that it's safer to take the bus from point A to point B using statistics that are generalized over time and geography.
For example, 30% of motor vehicle fatalities are alcohol related, and the vast majority of those fatalities take place after most people are done commuting for the day. Uber probably has a significant impact on preserving human life, after dark.
The purpose of the anecdote is to illustrate how those stats relate to decision making and risk/reward management by the travelling public. Am I at more risk driving three exits down the highway vs. crossing a busy avenue, sitting at a bus stop, riding a bus, crossing three other busy streets? I don't know -- and those statistics that you are citing don't answer that question. My guess is that I'm safer in my late-model car in a typical automobile accident than in any traffic or crime incident in the bus case.
> In my personal, typical case
They may not tell that story in this particular case, but unless something is wrong with the way with the statistics are gathered, it does present a better top-level picture than personal anecdotes. (While personal anecdotes can also be useful in understanding how to design around edge cases, but are not useful when figuring out the best way to design a system).