I worked with a very dedicated breastfeeding mother who asked a similiar
question to why give iron to her premie after discharge, her baby was
spitting up also.
After much investigation, by talking with knowledgable people because I
could find little in the literature, the conclusion was premies do need
additional iron because they did not store it in the last weeks of utero
because they weren't there.  It went along with Rebecca Black's comment
in avoiding anemia at all costs in infants.  The premie is at additional
risk for anemia.  This mom tried various options and settled on mixing
breastmilk with the iron and p. syringing it  at the breast or using a
cup, diluted in breastmilk it stayed down easier.  My understanding of
checking for anemia is a little more involved than merely a  finger
stick, so that needs to be taken into consideration.
I would like to continue to hear more on the controversies of iron.