14K gold is made of 14 parts gold and 10 parts of some other metal.
Gold is often mixed with other metals to give it a specific color, such as white gold.
Metals used to alloy gold are silver, copper, nickel, platinum, palladium, tellurium and iron. It is one of these metals that is causing the black marks.
It is likely to be silver or nickel that is the culprit, and there is no good evidence that this is related to iron deficiency. It may have more to do with the acidity of the affected person's skin.
Here's an article in Prevention magazine where they tested this phenomenon and fournd only one of seven people who got a black mark from 14K gold was actually anemic.
An MD they asked explained it was like a reaction to skin chemistry.