Using AI as a research assistant promises to provide significant benefits to researchers in terms of time-saving, efficiency, and reduced workload. However, as is well known, AI generated content and outputs are unreliable. Hence human supervision and oversight of the outputs of AI are necessary to perform AI-assisted research ethically. This paper argues that proper human oversight and supervision of many significant research tasks performed by AI research assistants involve, in many ways, performing the very tasks that were meant to be outsourced to AI in the first place. This is the paradox of ethical AI-assisted research. If used ethically and responsibly, AI does not provide significant net benefits in terms of increased efficiency and time-saving for researchers. But then there is relatively little gain in using AI as a research assistant. I then highlight significant risks for researchers and academics who engage in unethical AI-assisted research. Finally, I claim that the role of AI in ethical and responsible academic research should be reserved for secondary, as opposed to primary, research tasks.