Did you not read my example? We are talking here about multiple, physically separated exchanges.
Example:
Vanguard sends a buy order of 1000 shares of AAPL to exchange A. Some HFT firm sees that order on exchange A and knows that it will also be placed on exchange B, and was surely broadcast from Vanguard's trading floor at the exact same moment as the order to exchange A.
However, the HFT firm also knows that Vanguard is physically closer to exchange A then B, and the HFT firm has invested a lot of money to ensure that they have the physically shortest possible route from themselves to exchange B.
This allows them to broadcast their order to exchange B and have it arrive there before the order broadcast by Vanguard, even though they broadcast their order later.
It is somewhat difficult to wrap your head around, but it is a physical reality, and people are making millions of dollars from it as I write this.