Generally true, but safety is also proportional to the engineering. The early 2000s Ford F150 was big and heavy, but it was also a death trap compared to well-engineered cars that weighed half as much.
But, yes, all else being equal, mass usually offers more protection.
Where the hell did you ever get that idea? The two-ton cars of the 40's and 50's were death traps compared to a one-ton Honda of today. Volvo? Mercedes? Extremely safe, yet not "heavy."
....but safety is also proportional to the engineering
Extreme and rare example,: a Corvette or Lotus Elan, which absorbing all the energy of the crash when their plastic bodies shatter, allows the driver to walk away unscathed.
Looking for Danger? Mix traffic with high-bumper SUV's, 18 wheelers, and pick-ups on the road with lower passenger vehicles. An 18-wheeler is going to have more trouble flattening an SUV than a Honda Civic, but there's a good chance the number of dead will be equal.
Americans DO NOT know how to drive. They are rude, and careless and reckless.
Unfortunately, compared to the Vaterland, we Yanks ARE horrible drivers. OTOH, when they do have an accident in Wurstland, everybody dies, especially on the Autobahn! But in accidents and deaths per mile driven, we are way down in the international rankings, not the least reason being the amazing prevalence of drunks operating motor vehicles in this country.
We'll see how this changes as Achmed and Fatima (and the other wives) pack the 12 children into the old Opel and set out on the Autobahn. Especially if they dumb down the license requirements so as not to discriminate against the Turd Worlders overrunning Europe.