If you take a lot of flash photos, with the flash pointed directly at the subjects, you'll notice that eyes only sometimes go red: it depends on the angle of the eye with respect to the flash & lens. If the eye is facing off to one side, or outside the main area painted by the flash, it may not appear red.
Having one red eye could happen if, for example:
- the person is quite close to the camera
- off to one side of the frame
- not looking directly at the flash/lens
- has a lazy eye (or is otherwise pointing their eyes in different directions)
I would recommend checking more photos of the person (if you have more), to see if they consistently have just the one red-eye (the same one each time).
If in doubt, I would suggest to the client that 'it can be a symptom of eye problems, you might want to get it checked by a GP', rather than suggesting cancer straight up. The link you provided doesn't suggest it's unequivocal evidence, and pretty vaguely suggests that (for one red one black eye) "This can also be a sign that something is not right".