It's wrong to assume that the woman is lying off the bat, but it's also naive to think that some women don't use these type of allegations as a means to get paid.
The problem lies in assuming that the most common and likely explanation in these situations is that the woman is a liar motivated by money. Many people seem to respond to these stories as though that's the Occam's Razor solution to the question of what really happened. That's a problem.
There is overwhelming evidence that sexual assault and generally aggressive & disrespectful behavior by men, particularly men in positions of power, against women is a disturbingly common problem. What's more, it has been and remains a problem that is under reported, infrequently prosecuted, and often not taken seriously until multiple allegations have been brought against the same person.
In that societal context, there is value in demonstrating to the women around you -- not just to the women who have brought these accusations in a high profile context -- that you will listen to and believe women who speak out.
When anybody, but especially men, responds first and foremost to these types of stories by questioning the motives of the woman, they signal to the women around them that they are inherently suspicious of women who accuse men and doubtful that other men can or will engage in this type of conduct. That only serves to make it easier for the relatively small percentage of men who engage in that conduct to keep doing so, and thereby cast all men in that light.