Also, wtf is an 'unmistakable African accent'?
Note that I didn't say THE African accent. I appreciate that it's a huge continent, but there are (at least to a British/European ear) a lot of distinctive facets to pronunciations and intonations commonly used by many people from a number of countries across the continent. I would say the same about South America, North America, South-East Asia, Scandinavia, the Baltic States etc - there are, of course, many differences, but to an outsider, there are also distinct similarities.
I agree with PPs that 'Africa' is used as a lazy default far too often. Not to be flippant, but whenever they have world geography rounds on Pointless, huge, highly-populated African countries will invariably score very few points, along with tiny, relatively remote island nations and much of Central America. I know it's a UK-based programme, but I wouldn't say the same is true to nearly the same extent of much of South America and Asia.
A lot of people in the 'West' have very poor knowledge of African countries and would doubtless struggle to find any non-coastal African country or city on a map. Maybe it's used as a shortcut: instead of saying "She's from Liberia." "Where's Liberia?" "It's in west Africa." - people anticipate the likely response question and just go straight to the answer.
It's not right at all, but I suppose there are certain countries that have forced themselves and their culture/language on most of the world, meaning that they are much more (in)famous throughout.
It's a very valid point, though.