For C: "Basic to the whole disastrous situation is the fact that ..." is very close to the words in the original sentence - "The root cause of the crisis is that ...". And "the legal basis for asylum dates back to a time when it was almost impossible for anyone to seek it" is also very close to the words in the original sentence - "the legal basis for asylum was drawn up when very few had the means to seek it".
Against D: It paraphrases the second part of the sentence, but it omits the idea of the fundamental cause and adds the idea of the unexpectedness of the crisis.
You're right to think that D is a closer paraphrase than A, B, or E; so the fact that you thought the answer was either C or D was understandable. But when dealing with this sort of question, imagine the examiner writing it: first, he or she writes the correct paraphrase, and in doing so identifies the main bits of information that must be conveyed by a successful paraphrase. Having done that, writing unsuccessful paraphrases is easy: just take the main bits of information and either add new information, embellish the information that's there, or omit that information.
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