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I think the better way of saying it is that Galileo does not need PROGMEM.
With Arduino, the storage area (SRAM) for the sketch is small(2MB), so some libraries use the PROGMEM to move parts of their library (like strings and other constants) into the Flash to free up the SRAM space.
Galileo is not limited by SRAM space. It is much larger (256MB) than any Arduino. Granted it has to share this space with a Linux OS, but the Linux OS also brings along page tables, which makes the memory essentially much larger.
So, running the progmem example makes about as much sense as trying to use a Ethernet shield. It just is not needed.