They absolutely write it off. They just don’t make money off it. They say they made a dollar and then donated that dollar so they are asking not to be traced on it. It’s no different than if you sent the charity your $0.57 directly. You can even still write off what you donated. The only notable difference is that the company can say they donated to charity. And some do provide additional funds.
If they made money off of the donations then why wouldn’t every single company just ask you to donate to charity? Because they don’t and it costs money to take in donations. Often, companies that do it do it for the perceived goodwill. Good PR.