Agree - it's not worth it. Surely you'd far rather be here tomorrow saing you wished you'd run, than the opposite situation where you wished you hadn't run? If there is something wrong it may just put you out for longer, but if you don't run at least you're not running that risk. Even if all that is 'wrong' with you is that you're a little dehydrated from the sickness, or that the running motion will irritate your stomach I think a rest day is best for you...
But it's hard not to run when you really want to/feel you should be!