Imagine the following scene: The height one player can reach on jumping depends on how much time the button for jumping is pressed. When the player jumps, the input is sent to the server and physics are updated.
Now, imagine that for some reason, one input packet is lost or due to lag it begins to arrive late. From the point of view of server, the player is not jumping anymore, and its character will start its fall. Every other client will receive this information and let the character fall. Then, a new packet arrives that corrects this problem. From the perspective of the player, the character is still jumping. Maybe, thanks to this extra input the character can reach a higher slope. But from the point of view of the server and rest of clients, it wont make it.
This could happen, but online games that i have played (except for long jumps and high lag) it doesnt happen. My question then is: How does the server handle this situation? It cannot wait forever for input, it must update physics and acknowledge other clients on what's going on.