No. The borrow checker rejects programs that are definitely incorrect. It does not require that the program is correct.
That's a big difference.
The BC will not incorrectly approve an incorrect program.
But the BC does not approve all correct programs. Because some patterns which are indeed perfectly correct and will never explode the BC is not able to prove that and therefore the BC rejects the program.
The BC is effectively incompatible with typical video game patterns. The whole level/frame life cycle is effectively unsupported by the Rust BC. As just one example.