Maybe the confusion lay in the fact that this phrase is an idiom. When somebody says that another person (or they themselves) were at the "wrong place at the wrong time," what they mean is that something bad happened that was not their fault(s) at all. I've noticed this for a while. I think the phrase should be changed to suit the situation. For example, "wrong place at the right time," "right place at the wrong time," and "right place at the right time." All of these phrases would refer to an event that occurred unrelated to any activity of the participant or victim that would lead to them causing such an event. In other words, regardless of the phrase used, what happened there was none of their fault(s).

Something tells me I just made it even more confusing.

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"I want...to kill...all...white people."
--Barack Obama, out of context.