> Statistics, as a discipline, is essentially predicated on the principle that the objects of study do not know that they are being observed.
There is no such "principle" in statistics. Statistics is based on statistical methodology, i.e. formulas, models, and techniques that are used in statistical analysis of raw research data, which is collected, organized, analyzed, interpreted and presented. The Hawthorne effect, "a type of reactivity in which individuals modify an aspect of their behavior in response to their awareness of being observed,"[1] arose from analysis of a statistical study.
> Without this assumption, the domain is now more accurately described as game theory.
Game theory is utilized for decision-making in strategic environments where rational agents interact with each other. Statistics, on the other hand, is employed for reasoning in non-adversarial settings where the samples are assumed to be generated by some stationary and non-reactive source.
> Statisticians will happily and confidently ignore this and draw very wrong conclusions as a result.
Contradiction. You've already claimed that statistics is "essentially predicated on the principle that the objects of study do not know that they are being observed." Yet now you're claiming experts "confidently" ignore their discipline's "essentially predicated" principle.
[1] https://en.wikipedia.org/wiki/Hawthorne_effect