No, that's untrue. For instance, Rust doesn't prevent an out-of-bounds access at compile time; it just converts an out-of-bounds access into a panic at run time. That is, it reliably aborts the program (or the thread), instead of reading or writing out of the bounds of the object.
The same for "NULL pointer dereference"; the Rust equivalent (without using raw pointers, which require "unsafe") is calling .unwrap() on an Option<T> which has a None, which once again is not prevented at compile time, only converted into a panic at run time.
Edit: note, however, that idiomatic Rust can help prevent these bugs, by using iterators instead of indexed access, and match/if-let statements instead of unwrap/expect.
There's quite a huge difference between undefined behavior (dereferencing NULL or indexing out of bounds) which can lead to remote code execution and other super nasty bugs, and runtime checks which panic and abort the process reliably and in a well-defined way.
The same for "NULL pointer dereference"; the Rust equivalent (without using raw pointers, which require "unsafe") is calling .unwrap() on an Option<T> which has a None, which once again is not prevented at compile time, only converted into a panic at run time.
Edit: note, however, that idiomatic Rust can help prevent these bugs, by using iterators instead of indexed access, and match/if-let statements instead of unwrap/expect.