There is nothing wrong with a lawyer bringing this up publicly, as long as the client does not care. It happens all of the time.
In this case, there are good reasons to make it public, not the least of which is to keep us all informed about who we are dealing with. I, for one, would be hesitant to consign books through Greg given this information. If he breached an agreement with QC, who is to say he wouldn't with me on a consignment?
Mark is serving his client AND the community by letting us know all of this. Greg is, of course, free to defend himself on the Boards if he choses to do so.
And, yes, you absolutely can have a contract that is not in writing. You prove it by testimony of what the agreement provided, as well as evidence of performance. As to how a judge or jury decides what the contract provided, they listen to the evidence and decide who they believe is telling the truth. Juries and judges decide "he said, she said" cases daily.
While certain contracts have to be in writing to be enforced, exceptions are made, such as where there has been full performance on one side of the agreement. Otherwise, you are opening the door to people taking advantage of others by receiving performance and then not performing their end while hiding behind the lack of a contract as a defense.