The story itself is clear that iron was available to Noah. The time discrepancy might pose a problem for dating the flood but not for construction of the ark.
I'm not disputing that the authors of Genesis believed that Noah had access to iron. What I'm saying is that this might be like me telling a story about Jesus using a mobile phone or Nero's love of the Unreal Engine. It would be true in the context of my story, but it would be a glaring anachronism if it wasn't done properly.
For those that have been bothered to do the work (I never have), the Bible can be used to give us a date for the flood at around 2500BC. The discovery of iron smelting/smithing was 1300BC or so according to the link provided earlier. If we were to move the flood a thousand years forward (and say it's a dating issue rather than an anachronism) then a chronology ends up with the Holy Roman Empire still existing today and other such strangeness.
However, when Genesis was meant to have been written (according to tradition, by Moses), was meant to be about 1300BC. Modern historians date a lot of the actual writing to a much later date. It's easy to see why people writing in a world where iron is basically commonplace might think it existed in the time they envisioned the flood events occurred in.