In a tournament where every single game is drawn ...

How would the tiebreaks work?

(I'm talking about round robin tournaments, so average rating of opponents wouldn't work.)

Pretty sure it would be one big tie for first.

Without avg rating it would be one big tie.  With average rating or performance rating, the lowest rated player would win

At a big FIDE tournament I guess they'd have to do armageddon games where White gets 5 minutes and Black gets 4 but White must win.

... which is why performance rating is never used as a tiebreak in round robin tourneys (as far as I'm aware, admittedly, but if there are some obscure rr tourneys where it is used, that is very unreasonable).

And everyone plays armageddon games against everyone else?

This is why all Chess tournaments should be one big armageddon. 

Well... then what if it's, say, a 9-person tournament, and at the end of the armageddon round everyone has 4 wins and 4 losses?

I'm not sure

i would like to know who cheated. then pin the blame on the lowest player and give the tourney win to the second highest rated player using mathematical and symbolic logic.

More Armageddon

Yes

Let's just say it's one big loss... for chess.

And one giant leap for mankind.