I work in the legal department of a large company, I don't handle HR issues, but my colleagues do. If it's like any corporation, its head staff counsel is already on this, not in terms of an investigation, but coming up with the plan in conjunction with the head HR person most likely. Mainly because the person in question is known and has a public profile, he's not Joe Cubicle who got ripped at a company outing. They are going to go over his employment contract and see if it jives with the ability to dismiss for cause in the state of employment. On Monday, some staff peon, someone in my relative position, will contact the liability carrier for the company. Then we will work with a senior person there and determine what the risk exposure is/might/maybe, and then we do our investigation.
We don't do a complete investigation, as we are not prosecuting attorneys. We balance the risk exposure, set up a reserve (basically guesstimating how much it would cost in case of a potential suit from either the employee or the plaintiffs if the employee engaged in any activities on company time/tab (such as at conferences) and company equipment. The we balance out the cost of defense vs. termination. It's not typical that the company chooses to defend an employee. Its not typical that we contact the plaintiffs, unless they have lawyered up already and wish to file a claim/complaint for damages. Usually in the investigation of the employee, we can determine if they Did The Bad Thing, by our internal investigation. An even before we decide that depositions of all parties are necessary, we usually ask for all opposing counsels to submit their case to us, and we look at that. I don't work for a company with a media presence, but I know the PR people have a different employment contract that governs their social media use.
From that point, I can't really offer any insight to how Vox would handle it, as a media company, I imagine it would have different operation procedures than the company I work for, which is, financial in nature.
Let me stress this one last time. Staff Counsel/HR for major companies are not Law & Order: SVU Our job isn't "to get to the bottom of this." Our job is to protect the company's interests. Separate employees who present a risk. And do so in a way that mitigates the risk from the separated employee from trying to sue us. Also to mitigate the risk from 3rd parties who may want to seek damages.
Last edit: First thing any good manager (company man) does is tell every to STFU until they get word from higher up. And even then, they are usually given boundaries on what to say.