I'm not entirely sure I agree with this premise - there are lots of reasons why you might do that, including an excess of caution and deliberate misdirection.
However I think it's probably a given that they have dirty bombs. I mean really, it isn't any big technical achievement to build one - you just need a supply of medical or industrial radioactive material (available in any large city) and some kind of explosive device (ditto). Getting the optimal dispersal pattern would be a bit harder, but getting something that would cause widespread panic wouldn't be hard at all.