I don't think it's even true without market distortions. The whole point of BI is to give people without adequate income some means to support themselves. In other words, it changes the compensation to our hypothetical woman from $0 to $X,000.
At the margin this will certainly cause people to drop out of the workforce. Heck, as I get closer to having enough assets saved to be able to require, I'd probably choose the pull the trigger on that decision sooner.