Most people with 'hazel' eyes do have eyes that change colour. Most often it's a matter of greenish to brownish, occasionally including amberish or greyish shades. I have also been acquainted with one woman with blue hazel eyes -- sometimes they were quite blue, sometimes greenish, sometimes grey.

Light conditions, and colours near the person's eyes, do seem to be the main factors in what colour changing-hazel eyes appear. But then it's typical for various emotions to cause someine's eyes and/or pupils to narrow or widen, all of which tends to affect the play of light around the iris; and a variety of emotions can cause someone's skin to flush or pale, which could, conceivably, make the colour of their eyes appear to shift as well.

I'm not saying that those godawful badfic conventions aren't godawful, mind -- I'm just saying that there's (sometimes, plausibly) a reality buried under all that lurid prose.