You can overwrite an Intel chip's microcode from BIOS? I guess that means you could turn a Pentium into a chunk of useless metal too, with a virus (by writing a junk microcode into it). Or, simply turn the Pentium into a trojan.
Part of the delivery package can have the encrypted code to update the microcode inside the processor. The BIOS itself is necessary to talk to any device (it translates code or OS drivers into the hardware language) and the BIOS update fixes bugs in the BIOS as well. If the bug exists at the BIOS level, all operating systems will have the same problem, for example.
BIOS updates have had processor microcode update capability for quite some time now, but processors rarely need microcode changed.