Why does BitConverter.LittleEndian return false on my x86 machine?

Welcome to CLR Week 2013, returned from its two-year hiatus. A customer reported that when they checked with the debugger, reported even though they were running on an x86 machine, which is a little-endian architecture. The bytes are extracted in little-endian order, despite the claim that the machine is big-endian. "I don't get it." I d...