Through a lot of confused debugging, I found out that the following part of the documentation for RUSTC_WRAPPER is not, in general, correct:

Instead of simply running rustc, Cargo will execute this specified wrapper instead, passing as its command-line arguments the rustc invocation, with the first argument being rustc.

The first argument will in fact be the value of the RUSTC env var, if that is set. I don't know if this is intended, it is certainly not what I expected.