1. Maybe so, but your info is still anecdotal, and may be affected by confirmation bias. Also, the race of a driver doesn't necessarily say much about their nationality. I lived in Mexico for several years, and have traveled extensively there, and there are many, many Mexicans of European descent (and fewer of Asian, Middle Eastern, Jewish, etc descent), who you could never distinguish from your run of the mill white American or European just by seeing them physically. I'd be rich if I had a quarter for every time one of my Mexican friends gets told "but you don't look Mexican" here in the US. A Mexican cop won't assume a driver is a foreigner just because he's "white;" in Mexico, he's more likely to just be Mexican, unless maybe he has Nordic coloring.

2. The news cherry-picks what is newsworthy. For every American stopped by a corrupt cop in Mexico, there are hundreds of thousands who weren't, and which the news didn't report on. My experience is that things are never as bad as they appear on the news, and in Mexico I have tons of first-hand experience to confirm this when it comes to American perceptions of Mexico.

3. We'll have to disagree on this one. I've tried both, and renting a car always turns out to cheaper (unless you're alone), more reliable, more flexible, and allows you to do way more than relying on the other stuff you mention. There are lots of cool places in the Yucatan that are inconvenient to get to without your own car. I now rent a car every time I go to Mexico, except maybe in Mexico City.