So, obviously, I should read all the links given in the entire thread before posting, even though what I posted wasn’t untrue, just incomplete. 
A word on accuracy of information in textbooks: My fourth edition Atkins was published in 1990. Likely, nothing reviewed in the literature after 1980, was included in the textbook, which means nothing discovered and published after 1975-ish was included… which includes this Pitzer theory (according to this 1999 paper about Iron Mountain water, the Pitzer theory was published in 1977.
(I mean, hell: that paper was published in 1999. The water samples in question were collected in September of 1990. You do the math :))
I’d bet the Pitzer theories aren’t in the fifth edition Atkins; they might be in the sixth edition, depending on whether they’re too complicated for P-Chem students. (Pitzer is listed in the references as having published a thermodynamics text in 1995 which, I bet, has this information in it.)
Anyway…
Look at Table 1 from that paper (choose the full text in HTML link, and scroll down to near the bottom). You’ll see calculated activity coefficients ranging from near 1 up into the thousands. Obviously, activity coefficients that high would allow for negative pH–down to about -4 in this case.
I’m actually impressed with the precision of their calibration curves, as well, which tells me that this is actually real, and not somethign that’s been fudged out of the data.
So, the answer to the OP is:
Yes, you can have a negative pH (and, presumably, a pH higher than 14). It’s due to a very high activity coefficient caused by (AFAICT) intermolecular forces of some sort. However, these extremely low and high pH’s are not the result of simply having 10^(-pH) M hydrogen ion concentration. Note especially that the solutions from the Iron Mountain mines were also extremely high in iron and other ions, which increases the ionic strength, which increases the activity coefficient, which decreases the pH.
Thanks for pointing out that link, robby.
LL