Actually, he's right. You do know what PID is right?
Basically it's like when in a friend's chat. 2 People kicks at a really close time interval, of course 1 comes out on top every time. Guess who has the PID? It's the same with boxing, who gets the hit first? The one with the higher PID.
Runescape doesn't track the 0.01 second time difference between 2 characters picking up at an item, at least the time interval isn't that small. So it comes down to pid.
Since you're never really prepared with PID when in a drop party, you should just know where to click. By that, I mean click right on the center of the square. Some items are slim and long, some are big. You'll misclick a lot if you don't do this.
SM321 is right, but it's not always the case. Hosts have figured this out ages ago, and some don't like it. I personally would drop right after I click to another square, not when I come to a stop. But it all depends on how far the host is also walking, if he walks 2-3 squares away, it's more likely he drops it where he stops.