Anchoring is a more general marketing concept that works well in advertisements (crossing out a black $280 and putting a red $100 underneath it). Anchoring doesn't work so well for something much more fluid (and with much more at stake) such as a salary negotiation.
In-person sales meetings (which is what an interview is, for both sides) are where "first to talk" come into play. It's a concept as old as war meetings between opposing roman generals. First to talk loses, period. Why? I don't know, but years of sales and recruitment has taught me that whoever slips is going to give the advantage to the other side of the table.
You can only hurt yourself by giving a number. The company has set a budget, either you fit or you don't. Maybe the budget is higher than you expected and you take the job for way more than you would have asked for. Maybe it's less and you don't take the job. The key point is that company is not the only company you are dealing with - you can move on to another. And another and another, and as long as you don't give your number, you will win out.
I can't share this data but when I worked at a bootcamp our analysis showed this as well. Students that gave their number got paid less. There's a big push for bootcamp transparency so hopefully that sort of info will get published soon.