[whatshisface]

The chain isn't this:

Choice of how to measure -> History

it is,

Choice of how to measure + physical system -> Observations -> Interpretation of observations -> History

The choice of what and how to measure will influence the history you conclude, but that is true of actual "Caesar and Napoleon" history too, and in that case it's definitely not that past events are being changed, instead it is your knowledge of them. A really interesting principle is that any philosophical question that can be phrased without referring to ideas that only exist in quantum mechanics can usually be answered without referring to them.