Comment below rating threshold, click here to show it.
1.Cheat, you make more money than you lose that way. The rules are actually set up as 20% of your current(not total) winnings. Riot is setting a precedent that cheating is frowned upon, but is still worth it in the end. Had AZF lost they would be walking away without a chance to win the entire tournament, and still less money than they received after being fined.
2.This is not about the money. Riot is not budging on this schedule thing, and refuses to do an actual respectable rematch between the teams. I'm not asking for DQ, even though teams have done less bad things and got DQ'd.
3.The fans didn't want AZF fined 20% of their money, they wanted them either DQ'd or to have a rematch with TSM. This is not just a TSM fan-boy thing but think about it this way. If one team cheated heavily in the NFL, do you really think it's okay to still let them win that game they cheated for and possibly get world champion without even a game restart?
4. Extending the world championship for the rematch would benefit Riot and the fans. Many of your fans are willing to stick with the stream later on to continue watching. Riot on the other hand stands to earn more money from viewership during this period. It really is a win: win situation.
TL;DR: Riot's mistake with the minimaps was not only bad, but their handling of the situation promotes cheating in some ways. Fans didn't want to see a fine, they wanted a rematch or DQ.
Edit: http://na.leagueoflegends.com/board/....php?t=2663221 is their explanation. They explicitly say the Dyrus and Chaox looks had 0 gameplay implication (Done after the game was announced to be rematched) for the nay sayers, while explaining AZF's did in fact make a major difference. (Done after the other game was remade, this was in the middle of an ongoing un-rematched game.)