I've had this problem since day 1 of owning my car. We don't have acid rain or anything like that here...and its only on my bumpers.
did you buy your car used? if you boght it new and it came like that then you'd have to prove that it came of the lot like that (difficult).
since the problem is only on your bumpers, my guess would be that it's bug splatter (hence used). i have this problem with my celica (and it may be your problem as well)..for some reason almost anything tends to stick to the celicas paint in an unnatural way (it just gets gooey and spotty if you don't wash it regularly faster than what i've experienced with any other car).
i would still get a mother's clay bar--it's pretty cheap and its worth a try. like i said it's most probably bug splatter so it'll come off. your bug splatter will still feel smooth to the touch (since i assume you've washed your car numerous times), but that doesnt mean its beneath the clearcoat.