That's a nice chunk but insufficient nowadays. (The 24-year old in that article might've been able to make several $million in his remaining career.) The Lyft driver could still end up on the hook.
It's certainly possible, but it's unlikely. The Lyft driver's own assets are likely small, and most lawyers suing the driver would rather settle for an amount within the $1 million insurance policy, rather than risk getting nothing by going to court to try to get more than the insurance policy.
Even many doctors don't have malpractice insurance above $1 million (depending on speciality and state) -- most policies are $100K-$300K/claim, $1MM-$3MM/all claims (http://jop.ascopubs.org/content/3/5/274.full). So Lyft is providing more liability insurance than many doctors carry.
If you're demanding absolute 0% risk for the Lyft driver financially, this would not cut it, but very little anywhere is absolutely no risk.
"Commercial" is only expensive because higher mileage is higher risk. If you aren't doing a lot of miles per year, it won't be more expensive. Lyft's insurer probably has some mileage math worked into the premium. Or Lyft self insures and knows exactly how much mileage they are covering.