The 'Windows Experience Index' does not need anything - it has no feelings. In the sentence 'Your Windows Experience Index needs to be refreshed.' the 'to' does not 'belong to the 'need'' or 'belong to the 'be'', the 'to' belongs to the sentence 'Your Windows Experience Index needs to be refreshed.' I suppose it is a faulty sentence from a perfectly logical point of view - but language is not mathematics, it is not always logical.
I'm sorry, but I do not actually see a confusion here.
