Theoretically, when the market offers me an order book and I take offers on one or the other side that should be totally fair? I think until execution/fill the information should be totally between me and the exchange and no one else, right? I get that if I send a limit order that can not be filled, that that affects the market because new information is introduced (before the trade) but in the previously described case all the information going out should be after the trade already happened, right?
Sure, if you want to cross the spread you can usually get a clean fill in exchange for a bit more cost. That said, a fair price is fairly synonymous with a midpoint fill, and if you have a proper execution route you can get the ask (smart algo peg orders for example).
There is a caveat though, which is that top-of-book liquidity is increasingly thin every year. It doesn't take that much size to hit the bid, take out the first thin onion layer of liquidity, and have the spread widen away from you. If you look at the live order book depth you will see that the top of book is often thin and flittering. The deeper liquidity will react to the top levels getting cleared before you can blink. (That's why if you have a non-small order and want the bid price, sweep the bid and go a few cents under, you will get a much more reliable fill and won't be left hanging with the liquidity instantly repositioned a sub-penny below you).