mmmm ...... no - maybe I do this kind of thing for a living

You - nor I - have any idea whatsoever of what is happening with the Banks or at boardroom level, everything we know is mere conjecture. People have taken opinions and newspaper fabricated guesswork as fact and making statements that are factual - when they are absolutely not.
What we do know is that Hicks and Gillete own Liverpool - there may have been concessions regarding the actual sale of the club (even that is unknown) but Purslow is an employee of H&G, he may be running the day to day administrative affairs but he is absolutely accountable to the owners. He makes NO decisions without them. Broughton (by his own admission) is at his post solely to find and negotiate with prospective buyers. He has nothing to do with running the club apart from advising what would be attractive to a buyer. People can think what they like it's all guesswork.
H&G are running the show and will do until its sold. They do and will make the decisions. If they were not in control the club would already be in administration and its not.