Second, I don’t believe you. I say it’s always smarter to use the partitioned data than the aggregate data. If you have a data set that includes the gender of the subject, you’re always better off building two models (one for each gender) instead of one big model. Why throw away information?
If you believe the OP’s assertion
Similarly, for just about any given set of data, you can find some partition which reverses the apparent correlation
then it is demonstrably false that your strategy always improves matters. Why do you believe that your strategy is better?
Please avoid the biased default of Alice (female) being the assistant and Bob (male) being the higher-ranking person. Varying names in general is desirable, not only to avoid these pitfalls, but also to force ourselves to recognize that we tend to choose stereotypically white names that are not even representative of our own communities, much less the global community.