The fact that American Apparel's brand fired their CEO Dov Charney for misconduct shows that the Company will not support or tolerate misconduct among its ranks. They show their employees commitment to them and commitment to their consumers. As a company with social influence it is important that they demonstrate responsibility and ethics to the general public.
While a scandal involving high up members managers within an establishment can be embarrassing, and it may lead to some temporary loss of faith in a brand, the truth is that the consumers are what affect the brand the most. As long as the company keep making products that people are willing to buy, then the brand should continue to stand strong.
No, firing a CEO for misconduct does not harm American Apparel's brand, because it is important that the buyers know that they will stand up to misconduct. If anything, it helps the brand. American Apparel sent a message that they will take pride in their standards, and even apply them to the CEO. It's not a bad thing.
CEO or office clerk, misconducts happen and should be dealt with accordingly. I think a lot of companies brush issues with people who are high up in the ranks under the carpet to avoid embarrassment. In my opinion, treating a CEO the same as any other employee shows that there is equality in the company and can only be a good sign.