you are quoting from a FIDE Rule book.

The other KEY factor your forgetting is that notation is REQUIRED by the tournament rules except , wait for it,...., when its a scholastic event! If you can not rebuild the position from notation the position stands as is....

This is one reason I have always asked my students to notate games. In one case two kids i know would never lie said two entirely different things about a position. A pawn was on a square certain square or not. One kid notated , one kid stopped due to time trouble. guess who won the argument?

I have had situations where after a game a player said X happened after looking at notation. THe result stands even in FIDE rules this is true , a result stands. Your wrong Yerelov , and I am sorry that you feel differently. I also felt that TDs should beable to interfer with something like an illegal move, 3 move repeition , etc but someoen pointed out to me in the rule book you can not do this.   

There are two situations here:
What happens if a game is over and the position on the board was determined to be illegal? Does the result stand? answer yes

What happens if during a game the position on the board is determined to be illegal (ie two bishops of the same color for 1 side) but there is no notation to refer to determine where the error occurred?

answer the position stands as is 

 If you doubt me email the USCF and ask them your question and you will get the same response I gave you.

FIDE RULES are different but here are the FIDE Rules that are related to the situation at hand.

Article 8: Illegal Positions 8.1

If, during a game, it is found that an illegal move was made, the position shall be reinstated to what it was before the illegal move was made. The game shall then continue by applying the rules of Article 7 to the move replacing the illegal move. If the position cannot be reinstated, the game shall be annulled and a new game played. This applies to all sessions of play, and to a game awaiting a decision by adjudication. 
[Note that this discovery of an illegal move must be made while the game is still in progress, before resignation or the agreement of a draw. The only possible exception can be if the illegal move itself would theoretically end the game: anyone trying the trick 1. e2-e4 e7-e5; 2. Bf1-c4 Ng8-f6; 3. Qd1xf7 "mate" may be penalised under Article 10.17! Note that the act of playing an illegal move, at ANY stage of the game, does not IN ITSELF forfeit the game.]

8.2

If, during a game, one or more pieces have been accidentally displaced and incorrectly replaced, the position before the displacement occurred shall be reinstated, and the game shall continue. If the position cannot be reinstated, the game shall be annulled and a new game played.

"Most tournaments use FIDE rules."

Uh, not in the US they don't.  

It''s actually quite easy if you know how. just force the king to the edge with your bishop and knight.

you can only checkmate in the corenr the came colour as your bishop, so the enemy king will tend to run to one of the other corers if forced to the side.

this is the haredst part, it looks like the kings escaping but its noy.

Fine, you are right. 

The USCF is stupid for allowing this though.

An illegal game of chess is not even chess. 

P LACE YOUR OPENTS king ina  POSITION TNAT HE CAN NOT MAKE A MOVE

Place your oponents King in a position where he can not make a move

Same. It's as if all old threads are coming back.