You seem to be confusing "1-to-1" mapping, and "identity function". While the identity function is a trivial "1-to-1" mapping, it's not true every "1-to-1" mapping is the identity function.
However, even side-stepping that, Juerd doesn't mean byte values map 1-to-1. The mapping is after decoding. For instance, the UTF-8 byte sequence 0x82 0xC3 decodes to C2. Which indeed does map to the C2 Unicode code point.