There's always a risk of being a victim of a crime when hailing a ride from a stranger and while Uber/Lyft somewhat mitigate the risk, it's not completely safe either.
Author was also implying that they were visiting Russia. It's much harder to assess safety when you're not a resident, especially when you don't speak the language. And the fact that because many people in a culture engage in some behavior says little about its safety — e.g. riding scooters in Saigon, or smoking!
That said, on my last visit, I used Uber many times, as it's incredibly cheap and requires no negotiation. But don't be in a hurry. The horrible traffic and very wide, divided streets of Moscow make it particularly challenging to navigate to a passenger's precise location, so it can be an extremely long wait even when free a vehicle is very close geographically. Perhaps LibreTaxi would help solve that by lowering the barrier to entry and drastically improving the number of cars available.
Yes, Russia especially is one of those places where every car on the road is a potential taxi and a lot of people use them.
I haven't visited personally but friends of mine who have did tell about their experiences on hailing rides from strangers without knowing the language. Don't take my anecdote as a safety recommendation or evidence of it.
It's a matter of cultural differences.
Uber/Lyft provides you with a sense of safety, but if you end up being a victim of a crime in an Uber in Russia, I'm not sure how much they can or will help you afterwards.
http://www.victimsweek.gc.ca/res/r512.html
Men are overwhelmingly the majority of victims of stranger violence and robberies.
But... evolution dictates that we care more for women than for men.