Whole Pop Magazine’s website actually mentions this event in a bit about the toothpaste. And here is another Youtube link to an old English-language Darkie commercial. But the most comical link of all is the Wikipedia entry for Darkie, which includes this howler:

However, the Chinese name of the brand, 黑人牙膏 (in English, “Black Man Toothpaste”), has not changed; a Chinese-language advertising campaign reassured customers that “Black Man Toothpaste is still Black Man Toothpaste”. This is because the term 黑人 does not have any negative meaning in Chinese. The phrase 黑人 (hēi rén) in Chinese is a general term for persons of African descent.

While in many cases heiren carries no negative meaning, in many other cases it does. In the latter usage, it’s somewhat analogous to the term “Chinaman”, which Wikipedia admits is both neutral and offensive in meaning, depending on who you ask.