Several sources claim that a person's apparent eye color can change (primarily and perhaps only in lightness or darkness) as the result of mood changes, illness, or stress level. Your quoted article doesn't give any details about the reported eye color changes in patients diagnosed with MPD, so it's hard to know if they may be referring only to such a phenomenon, or making some loftier claim.
Some people have noted that when they are ill or under stress that their eye color becomes darker or lighter. (source)
Eye color does not actually change with mood. What does change is the way light reflects off the iris, creating the impression that the color of the eye has changed. . . . While light affects the retina, mood also affects retinal contraction. Under stress, the retina contracts, making the pupil smaller and revealing more of the iris to light. In lighter eyes, or eyes that reflect more light, this can cause the eyes to appear to change color. (source)
It is easy to find anecdotal evidence of people who's eye colors seem to change, allegedly according to their mood. Typically in those with hazel eyes, their eyes may appear blue (particularly when happy) or brown (particularly when upset or sad). Although it's unclear to me how much of this is truly related to mood, and how much may be environmental factors that affect the light reflecting off of the eyes. I can say that as a person with hazel eyes myself, I frequently have friends comment on my changed eye color. But I've never paid close enough attention to notice if my mood, the environment, or perhaps the sunglasses my friends were wearing were a common theme. :)
From The Merck Manual, Dissociative Identity Disorder (aka Multiple Personality Disorder) is "attributed to the interaction of ... overwhelming stress," and "patients often have a remarkable array of symptoms that can resemble those of anxiety disorders, mood disorders, posttraumatic stress disorder."
So it seems plausible that eye color can change, at least in terms of shade, by mood and stress changes brought on by DID/MPD. However, the closest I have found to a credible source directly linking eye color change to DID/MPD is in this review of this book on the topic of DID/MPD. The book itself appears to be well-received, based on the reviews on Amazon, including at least one by the spouse of a diagnosed "multiple" (DID patient). I'm not sure how much this all says about the credibility of the book, but at least it's not obvious poppy-cock, eh?
So it seems the answer is Yes, DID/MPD can cause temporary changes in eye color, at least if you accept that a change in the eye's shade counts as a change in color.