The Beaglebone Black CPU has some rather nice I/O coprocessors running at 200MHz - so it basically has that dedicated microprocessor built in.According to the Adafruit suite, the neopixels need 800 Khz (the earlier version based ont he WS2811 need 400 Khz), and looking at the code, it disables interrupts before starting to update all of the leds (which are done in a serial fashion), and interrupts are enabled after all of the pixels have been updated.
The code uses assembly language for the AVR to minimize any timing issues. They use different asm code for 8Mhz and 16Mhz AVRs and for the older 400 Khz WS2811 vs. the 800 Khz WS2812s.
For the Arm case, Paul has contributed special code for the Teensy 3.0, and if it isn't Teensy, it assumes it is a Due. Unlike the AVR, it looks like it is mostly C code for the arm.
Now presumably the native cpu on the Galileo is fast enough, but the problem is ALL of the GPIO's are done via a Cypress i2c expander, and the Cypress i2c port expander that does all of the I/O can only run at 100 kHz (the Galileo processor itself can also run i2c at 400 kHz). But even at 400 kHz, it is not fast enough, since each i2c transaction presumably takes a few bytes over the wire. The neopixel documentation says that other Linux systems on a chip like Rasberry Pi, Beaglebone Black, pcDunio, etc. have similar limitations, and that you really need a dedicated 8Mhz or faster microprocessor.
Just a 'simple' matter of writing a driver (those I/O coprocessors are only programmable with their own assembly language)...