Who's "they"? I'm having a hard time imagining people other than the most die hard public transit proponents or government employees of countries where few can afford cars saying that. Owning your own means of transit is something the wealthy literally everywhere do (though the minimum amount of wealth to do that is higher in e.g. Singapore than in Canada), if you're super wealthy you don't even drive it yourself.
I'm not criticizing public transit here (I'm a big believer in light rail) but your quote sounds like something out of left field.
Edit: Turns out I was sort of close, a politician in Colombia said it.
I think the point is that in a genuinely rich country (as opposed to a country where 0.3% are rich and 99.7% are fooled into thinking they could be if they just worked harder) the state income from taxes are sufficient to properly fund public infrastructure such as buses to the point where taking the bus is something you find yourself doing equally often as driving no matter what your income is.
In New York the head of my department was making $10 million a year and took the Metro North railroad to Grand Central and walked to the office every day.
personally, i interpreted that quote as being mostly about security. a rich person being able to ride the bus - or letting his/her kids ride the bus - without having to worry about being kidnapped for ransom by the destitute.
and you do have high profile politicians or celebrities in european cities (i only know examples from europe though) using public transport or riding bikes to get around.
