The thing that people want to avoid is getting too much iron, which
can lead to higher risks for certain heart problems.  When women are
having their periods, for example, they lose iron through the
bleeding.  This means that their average iron levels are lower than
men of the same age - and they have lower rates for heart attacks.
When they get older and stop having their periods, their rate of heart
attacks goes up until it is about the same as men of the same age.
Most people who are on low carb diets are eating enough foods that
contain iron (such as red meat) to get an adequate amount of iron, so
adding more from a vitamin pill is not recommended IN GENERAL.

It's worth noting that people vary.  What's good advice overall may
not be good advice for one particular person.  Although anemia is rare
in men, I have a long history of being borderline anemic.  So FOR ME,
a small amount of supplemental iron is useful.  I also donate blood,
so I get a free blood test for iron more often than many people.  I
try to keep it "just high enough to be eligible to donate".

In general, the RDA (Recommended Daily Allowance) of vitamins and
minerals is an amount needed to avoid deficiency diseases.  In MOST
cases there is no problem with taking quite a bit more than the
minimum amount.  The body simply gets rid of the excess.  But as noted
above for iron, there are exceptions.  The fat-soluable vitamins
(Vitamin A, for example) can also be a problem if taken in large
amounts.  But the body can easily get rid of excess water-soluable
vitamins.

Now, there are many people who believe that there are some vitamins
and minerals where the OPTIMUM dose is a lot higher than the RDA.
Vitamins C and E get the most publicity.  Taking "extra" zinc is
highly recommended by Dr. Atkins.  He recommends 100-150 mg per day.
Since the RDA is around 15 mg, he is recommending 700% to 1000% of the
RDA. So you should have no problems at all with a "mere" 250%
supplement.

Becasue a diet that includes plenty of meat already is high in iron.
Too much iron in your diet is not healthy.