Anecdotally speaking, I haven't witnessed things in their "The Russian Dash-Cam Supercut" video even once. I can confirm that lots of people disregard rules if they think they can get away with it, though. Things like not lowering speed before the yield sign or going full speed through the crossing on yellow traffic light account for majority of the accidents involving two cars. Crossing the road in the wrong place causes most pedestrian deaths.
Statistically speaking, we've got 3-5 times more fatalities than EU countries per capita and about 1.5-2 times more than in US, from what I've found. Some of these accidents happen due to weather and poor road maintenance, but you can't really blame the weather much, since the situation is much better in neighbor Finland.
Sounds like Boston...