Based on local soil conditions I very much doubt that the soil is iron
poor. However, anything is possible.

It certainly is. Giving a yellowed gardenia a shot of Ferromec has worked
several times for me, so it is worth giving it a try.

Here's more specific info on yellowed leaves:

"You often see gardenias with pale green and yellow leaves and this is due
to a nutrient deficiency (yellow leaves with green veins - magnesium
deficiency), (green leaves with yellow veins - iron deficiency). This
doesn't mean that the soil doesn't contain these nutrients, it means that
they are locked up in the soil and plant roots cannot access them."

http://www.abc.net.au/perth/stories/s1081361.htm