Suggesting the first figure is all about anchoring [1]. Once that first figure is out there it sets the tone for the negotiation. Many employers will try to offer you $current_salary + $small_delta. This advice is all about anchoring at a higher figure, breaking away from any relationship to your previous figure. So it's important you do say the first figure.
Also, the deflection is there to make the figure you want seem normal to you. It's no big deal you're asking for a whopping salary - that's just what you expect. The last thing you want to do is take a sharp intake of breath and make it seem like you're overplaying your hand. Just casually drop in $top_end_figure and move on with the conversation.
A great book on negotiation skills is "Everything is Negotiable" [2]. That book has literally made me thousands.
[1] https://www.pon.harvard.edu/daily/negotiation-skills-daily/w...
[2] https://www.amazon.co.uk/Everything-Negotiable-4th-Gavin-Ken...
Personally I try to start a discussion about how important benefits are to me, and the fact that they can make comparing salaries between companies meaningless, so I can't really talk about pay expectations until I have a good understanding of the full compensation package.
But I'd love to hear some other approaches to go to.
*Edit: Of course this isn't something I want to let a prospective employer know, so I try to keep it generic by referencing benefits.
https://haseebq.com/my-ten-rules-for-negotiating-a-job-offer...
I don't know if this is the specific article addressing that question, but this guys writing on negotiations was very helpful to me.