BSI primarily benefits sensors with small pixel pitch, and the aim is to increase QE (quantum efficiency), which only might affect noise levels as more of a byproduct of its primary job. (BSI basically "flips" the fabricated sensor upside down, putting all the R/C activation and readout wiring behind the photodiode, and therefor out of the light path from the pixel/microlens.) The pixel pitch on the 1D X sensor is relatively very large, and it would benefit little from a BSI design. The D800 does not use a BSI design either...it is still FSI.
The difference between Sony cmos sensors and Canon cmos sensors is that Sony integrates FAR more hardware-level noise reduction technology than Canon. Currently, to my knowledge, Canon sensors only employ CDS, Correlated Double-Sampling...however I believe their patents date back nearly a decade. Sony sensors employ a newer and more effective form of CDS, a form of transistor differential compensation to reduce FPN, integrated column-parallel ADC (a smaller, slower ADC for every column of pixels built right into the sensor...slower ADC's produce less noise of their own, and having one ACD per column also helps reduce FPN), and a few other smaller improvements that I currently can't find the patents for. Its these explicit noise reduction features that make a Sony Exmor sensor produce cleaner pictures than a Canon sensor.
Canon could benefit from a BSI sensor in their compact and bridge cameras, but the improvement to QE in a large sensor with a very large pixel pitch like the 1D X would be very small...maybe 1-2%...definitely not enough to put them in the same league as a Sony Exmor. (It should be noted that Canon uses a gapless "microlens" sensor design...but the pixels themselves still have gaps between them...most of the activate and readout wiring exists within the spaces of the gaps, with minimal intrusion into the light path from a pixel. If this were not the case, as might indeed be the case with a very high density full-frame camera (say 60mp or more, the 2-3 micron pixel pitch range), then a BSI design would probably benefit a full-frame high resolution sensor as much as it benefits a tiny point and shoot sensor.)
Your post needs more acronyms
Hah! I could probably conjure up a few more for ya... ;P