In most cases this isn't accurate. The author (or, more commonly, their agent) submits the book to several publishers, who either accept or reject or refer for edits. Unless you're in the top percentile of published authors, there's very little room for negotiation. It's pretty rare for an author to have more than one "accept" on a work simultaneously, many publishers frown on multiple submission precisely because it can lead to a bidding war.
The author always chooses the publisher. They might not have many (or even multiple) options, but there is no coercion and the author can choose to keep looking for a different publisher, to go with a lower-tier publisher, to publish themselves, to publish via vanity press, or not to publish at all.
