Of course it's possible. Say you would fork gcc (or clang) and teach it a few extensions for the C type system that allow some more safety checks at compile time (for example something similar to Rusts borrow checker). Since those checks don't change the generated code, you now have a language that's safer than C, but equally fast. Now you add some language primitives that make it easier for the compiler to understand the intend of the programmer, making it easier to optimize the code (there are already plenty of opportunities used by C extensions, like signaling that some if branch is unlikely to be taken. More opportunities exist if you modify the language more heavily). Now you have a language that's both safer and faster than C.
I don't want to make any claims about Rust performance in practice, I haven't run enough benchmarks for that. But it's perfectly possible that the statement could be true.
Maybe not faster than C but at least as fast while bringing modern patterns and better safety.
It's actually entirely possible. For example it's how Fortran has been traditionally faster than C, by not allowing for aliasing (which is also an unsafe feature) it can give the compiler more room from optimization.
That's from the linked article 'Rust is Software's Salvation' (bullet point 3).
That's C's limitation: it can only be as fast as the compiler geniuses can make it, or as concurrent as its users can explicitly make it. Given that almost all computers where you care about raw performance are multiprocessing now, that's a huge deal. Languages with primitives like async/parallel map() are going to have a hard time keeping up with those that do.
Sure, you can write ultra fast code in C or assembly. The fastest way to do so might be to write it first in Erlang, Go, or Rust and reverse engineer it from the resulting machine language.
(It's not built in, but that's a good thing IMO. :-))