Reminds me of a Belgian guy who was in the papers a few years ago, who had to pass an 'integration test' before he could get Dutch citizenship. Part of that test is a language test (people from the north of Belgium, i.e. Flanders, speak Dutch - it's the same language as the one spoken in the Netherlands. So, like the woman in the OP, he had to take an exam on his mother tongue, and with much less of an accent than an Irish accent is as compared to the Queen's English). If you have a degree (even just a high school degree) from a Dutch language school, you're exempt, but this guy didn't so he wasn't (this exemption was put in to basically avoid situations like this, under the assumption that the vast majority of people would have a high school degree).

Either way, he failed the test a few times; reason being that this 'integration test' doesn't just cover language skills, but also things like 'knowledge of Dutch society'. For example, you get 3 pictures of a front yard of a house, with varying degrees of clutter on them (like a children's bike and a garbage bin with the lid open). Question being: how are you supposed to maintain your yard, like in picture A, B or C? Most (Dutch) people I've given the test failed it because the questions are so ridiculous. It's quite lulzy actually. Well not for that Belgian guy I presume.