It's not the same unwritten social contract: in Rust even the unsafe code has the same stricter type signatures as the safe code, so there is a formal way to judge which part of the program is at fault when the contract is broken. You might say the contract is now written. :-)

In C, the type system does not express things like pointer validity, so you have to consider the system as a whole every time something goes wrong. In Rust, because the type system is sound, you can consider each part of the program in isolation, and know that the type system will prevent their composition from introducing any memory safety problems.

This has major implications in the other direction as well: soundness means that unsafe code can be given a type signature that prevents its clients from using it incorrectly. This means the set of things the compiler can verify can be extended by libraries.

The actual practice of writing memory-safe C vs memory-safe Rust is qualitatively different.