If it clearly benefits current and future victims to be taken seriously and get any help they may need? Yes, in my opinion. But that is a much more personal ethics call.

Except telling someone like the OP who clearly is not the kind of person that would believe the victim or try to get any help, and instead launch into a cross examination isn't going to do that. All that's going to do is make the victim feel even worse, and possibly discourage her from getting help or reporting at all.

The fundamental principle of the American justice system is that we should be skeptical of all claims of wrong-doing. The appropriate response to these claims is to ask for evidence and in its absence potentially educate the claimant on how to properly collect evidence. I'm sure there's a lot of legitimate claims out there, and most of them will not result in justice. However, rampant speculation based on Twitter anecdotes is never going to be helpful.

Except that's for the Justice System. Not normal people. The Justice System can take care of vetting evidence. Normal people are supposed to be supportive and stand up for those who come to them with stories like this one.

And I'm sorry, but if someone comes to you and says that they've experienced the things in this story, and the first thing you do is ask for evidence, then you will be branded a monster, and rightfully so. You are telling that person, "I do not believe you; I think you are a liar." If someone comes to you with a story like this, you provide support to them. You console them. You ask them what you can do to help. You do not cross examine them, and make them feel terrible for coming to you.

Different audiences. If you're a close friend or the HR person at the corporate office, then sure the first thing you do is console them. If you're the media or just general public, you ask for evidence before you socially/publicly crucify someone.