Access to cheap iron definitely is widely accepted an aspect of the bronze to iron age shift (well, obviously, but rather rejecting the idea that iron is "superior" to bronze in any way other than cheap access to iron even when the economic implications are so clearly visible in the archaeological record), but it's important to remember that virtually all aspects of life changed for people in the mediterranean around this time. It's very difficult to summarize the shifts as even potentially attributable to a single cause (like much of materialist history!).

Cause and effect are very difficult to differentiate, and combined with the fact that this a) produced a profound cultural change in the region (e.g. the rise of Judaism, the writing of the Iliad, the language shifts that occurred over the ensuing centuries) and b) distinguishing migrations from invasions from cultural trends in the archaeological record is nearly impossible, I highly recommend against such reductive narratives. Other possibly confounding variables include the spread of horse technology, trade technology (i.e. writing), climate and agricultural pressures, etc.