Why shouldn't they?
Most things people do are not done consciously. That's just a weird bias that we humans tend to have...most decisions will not be based on thorough consideration as this would take way to much time. When you have to decide which drink to buy, it will usually be gut decision. If we decide to put on a sweater, it will usually because we feel like doing it and not because we measured the temperature in the room. To me, all of those things would be intuition (I'm not a native English speaker, but since it's a Latin word, meanings should roughly be the same in other languages as well)...
About predicting social situations, this might be more difficult for Aspies due to wrong interpretation of social cues like EzraS said...on the other hand, aspies might notice tiny details that other won't, which could e.g. cause a (correct) negative intuition that NTs wouldn't have in this situation.