There is a brand of toothpaste in China called Hēirén Yágāo (黑人牙膏), or literally Blackman Toothpaste. The particular man that they chose to serve as the smiling icon of the company is wearing a tuxedo and a top hat, but is only vaguely black. I couldn't help but feel like there was something decidedly un-PC about Blackman Toothpaste. However, they don't translate the name literally into English; the name they use in English is Darlie Toothpaste, which on the surface seems innocent enough, but I was always a little suspicious that that originates from "Darkie".
Well, about ten seconds of Googling just resolved all my doubt.
According to this Wikipedia article, it turns out my suspicions were exactly right. The toothpaste was first created by a Taiwanese company and it was called Darkie Toothpaste, complete with a caricatured black man's image that seems to be exaggerating the contrast between his skin and his teeth. Wikipedia notes no uproar about it, but in 1985 Colgate-Palmolive bought the company that owned the brand and obviously couldn't have that among their new subsidiaries' products. The solution? First they changed "Darkie" to "Darlie" and later they changed caricature for a more dignified, only vaguely black image.
I'm still not convinced it's made the full jump to unoffensive. Let's say you take the most unoffensive literal translation: African Toothpaste. What the heck is that? The only way it even makes any sense is if you're contrasting skin color with how white the teeth are: "You're teeth will look as white as a black man's teeth!" Uh, yeah. How about Asian bananas? "Our bananas are fresh and always yellow like an Asian!" Or Native-American apples? "Red as a Native American!" And, in addition, if I saw "Darlie" and thought "Darkie", isn't that something that would occur to other English speakers?
And that, perhaps, is the rub. The branding isn't offensive in a Chinese context, while in an English context it is. Not being considered offensive in the Chinese context, however, is certainly not to say that it shouldn't be considered offensive. However, offensiveness certainly varies form language to language, and this is just one of many examples. (Another that comes to mind is that in many places people will freely tell you that you're fat, where in English that would be really offensive. China is also one of those places.)