They are focused on objectivity as connection with something outside the mind of the scientist, i.e., empirical data. Thus they explicitly separate the experimenter from the experiment, imagining that you could "swap out" any experimenter for any other, and have the same experiment. That is the crux of "objectivity". Consensus is something that eventually does emerge in science, just as in many other pursuits, but it is not part of the meaning of what distinguishes science from other, less objective, ways of knowing.

At the heart of the issue is how is science different from pure mathematics. We agree that there is considerable overlap, as science uses the tools of mathematics to the degree that someone has to fashion the hammers for the carpenter. But the scientist has a different means of establishing truth than does a mathematician. A mathematican needs only to establish "provability" to be finding truth in mathematics-- it's up to them if it is intended to model truth in objective reality (a la Hardy). The scientist, on the other hand, has only objective reality to tell them what is true, he/she chooses axioms to get that agreement, but the axioms never decide the reality-- experiments do that. All that is included in parts of that Wiki definition.

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