My DD had the exact same thing happen when she had just turned 2 years old. We couldn't figure out why - her older sister doesn't eat any meat and has HIGH iron levels, and this one eats tons of meat and has low iron! The mainstream ped we were using at the time got all in a tizzy over it and freaked us out.
So I started digging, researching, and family history and found that my mom has a near identical health history as my DD is having. She always had low iron and had constipation problems, just like my DD.
It's not that she wasn't getting enough iron in diet (a lot of kids who have low iron ARE getting enough iron). What we ended up concluding was that iron levels are NOT a one-size-fits-all diagnosis. Some people have naturally lower iron levels, and others have naturally higher ones. It's pretty normal in people to have a range, just adults aren't routinely tested for iron unless something is wrong or there is a medical issue, so people aren't usually very sure about their iron levels.
We switched to a holistic ped, who did heavy metals tests and some other testing to make sure it wasn't a problem and we found that she was perfectly healthy, but has a really high metabolism (she's also our tiniest baby, never seems to gain weight, but eats a ton). He put her on organic toddler vitamins and sent us on our way.

I wouldn't get too freaked out at this point. Mainstream docs tend to have a view that everyone should have the same levels of everything, but that's just not realistically how bodies work. Kids inherit all kinds of different things from parents and grandparents. If the low iron doesn't seem to be affecting your DS (if he's not tired all the time or having diarrhea), I would discuss with the doc that you don't feel it's as big of a problem as she thinks it is (and switch docs if you need to, since some docs get pretty belligerent when their "orders" aren't followed).
Good luck to you!