Sure. Suppose there's 8 on the best bid and then you send a limit buy order of 1 quantity to the same price, making it 9 in total after your order arrives. Then after that, suppose a trade is shown with volume 9 at that price level. What this event implies is that someone sold into the best bid and took it out completely. If this trade volume is fake in any way, then your order won't get filled. But in reality, that never happens on the large exchanges. Your order will always get filled when you expect it to, meaning that the volume is real. If the volume was fake it'd be easy to prove. Just put a limit order in the book, record your screen, and prove that you didn't get a fill that you should have gotten. That won't happen in the large exchanges because the volume isn't fake.
There's some misunderstanding here. The paper is asserting that the volume is fraudulent, due to wash trading, not that the trades are fake.
In your toy scenario, I put 8 on the best bid, you put in 1 more, then I go on another account and hit the bid for 9 volume. 1 of that is legitimate volume, and 8 is fraudulent because I'm trading with myself (aka wash trading). Sure you get your fill, but the paper asserts that the stated volume is too high (in this case by 8).
Sorry if it should be obvious. I'm used to being 100% stupid at least 10% of the time