i wouldn't believe that incredible power output from a htib. even most full size mid-level receivers can't output that much power.
power measurement is not about believism - my friend. you've got to measure it! You have to hear it. This is not religion per se.
IF you are in doubt - test it.
Size of your typical AVR will not be able to output that of course - since they still use the class AB topology - with your typical EI core power supply.
But it does not follow the HTIB I mention will put out less power than your conventional wisdom and cheap dig! :-)
Would you believe the amp has wimpy heat sink ? ha ha ha - it is driving my Bohlender X3 / X1 in surround mode!
I have the TDA-8950, would you know how much power it can deliver, given the size of the heat sink?
Lastly, 800 watts is not incredible nowadays. How about 1000W RMS HTIB? Super Incredible? Where are you this past years?