hifonics bxi 1206d amp

FWIW - it's pretty much accepted that the Hifonics brutus amps are over-rated.  I think the general assumption is around 20%.

Regarding your calculation -- you need to account for efficiency.

Assuming an average class d at about 75% you can drop that theoretical power down to about 850w.

However, fuses aren't that black and white.  An 80 amp fuse will pass 90A almost indefinitely, 100 for up to a few minutes, they can even pass 2x rated current for a few seconds w/o blowing.  Plus different mfg's might apply fuses differently - if a fuse is intended to blow at the first sign of stress it's probably going to be smaller (compared to rated power) than a fuse that's intended to blow only at the electrical limits of the amp. 

Add to that the low crest factor (big difference between Peak power and rms power) of music and it's easy to understand why an amp with a seemingly small fuse can actually produce quite a bit of power.

I know of one a/b amp with 2x30A that benchtested at 923w w/o blowing the fuses.

I think that's a realistic expectation.