Here are the two failure modes. Say you believe Alice, but she’s lying. Then Bob gets fired or moved despite being innocent. Or, you believe Bob but he’s lying. So Alice has to either leave (the exact same result as Bob), or continue to work with her rapist (arguably a worse result). The two failure modes are equally bad. From the point of view of minimizing social harm, you want to minimize the sum of the two failure cases.
Now, let’s look at the statistics. Rape is much more common than false accusations of rape. Now, you run a simulation using these statistics. What happens? The rule of believing Alice results in vastly more cases where you make the right decision than the rule where you believe Bob. And it results in vastly less social harm overall.
So what’s fair? I’d assume that you’d say it’s to believe Bob, since you have no “hard evidence” to the contrary. (To nitpick: a sworn statement by a witness, Alice, is evidence admissible in court.) But that means that 10-20 women are forced to leave their jobs or work with their rapists for every one man who is spared from wrongly being fired due to a false accusation. From the point of view of minimizing social harm, you’ve failed.
Of course, in reality, you’re usually going to have some other evidence to go on. Bob might say, “Alice is lying I was at the bar with my friends when the alleged rape happened.” If so then you should believe Bob, of course. The idea of shifting the burden of proof might not work in a criminal case, but for the reasons explained above, the considerations in a work place scenario are very different: false negatives are just as bad as false positives.