I'm kicking myself for not getting more verbose output logged when I had the thing in my hands. I did a successful read, and it appears that they hook the firmware EEPROM straight to the southbridge instead of going thru an EC for the Mini :-)
Here is a the read output I captured: flashrom v0.9.0-r631 No coreboot table found. Found chipset "Intel ICH7M", enabling flash write... WARNING: SPI Configuration Lockdown activated. OK. Calibrating delay loop... OK. Found chip "Macronix MX25L8005" (1024 KB) at physical address 0xfff00000. Reading flash... done.