It isn't uncommon to be given an acceptable figure, go through several rounds of interviews and end up with job offer but with a lower salary than initially agreed because the recruiter padded the numbers.
No, it doesn't lose the negotiation. What makes you think so? Setting anchors and controlling the document is very powerful.
But yes, you need to know what you can get, and you need to be able and willing to walk away.
> They're already anchored, because they know what everyone else is making.
Different people make different amounts of money.