http://collegecatalog.uchicago.edu/thecollege/economics/#pro...
Looks fairly rigorous. Can't say for sure, but it does appear that while you are encouraged to take the most rigorous calc sequence (typically required of math, hard science, engineering majors), econ majors are allowed to take an easier calculus track. That's pretty typical of econ undergraduate degrees - many universities do provide a slower, easier calculus track for certain majors (typically life science majors or social science majors).
I have no idea what track Nate Silver took, and of course I can't speak to the "self-labeled" engineer. I'd agree that an econ from a reputable school has some mathematical rigor, but not quite at the level required of a typical math, hard science, or engineering major.
Either way, I would agree with you that it is silly to say Nate Silver doesn't have a math background - clearly he does.