Someone else's high ping does not cause you to lag, nor does it cause the sever to lag.
This is one of the main reasons why I appreciate RO so much compared to some other games that I play online, it doesn't seem to have a problem when another players ping gets a little large, and I've always enjoyed how smooth game play can be on even a full server.
But just because I dont see this issue in RO doesn't mean I would go so far as to say it doesn't happen. For example, I help my clan manage and admin a Halo server in my spare time, and I have to consistently watch for players who are sporting less than average connections. It doesn't take a rocket scientist to see that the server can start to get a little wonky once a player with a less than average connection joins up, and it's easy to notice when things get back to normal after he leaves. Add that to the fact that I can witness the same sequence of events up to a dozen times a week, I feel confident it's not just a coincidence.
It's just going to send the packets to the clients, it doesn't care how fast they get them, it will send the packets at the same rate."
And this is all fine up to a point, but this explanation is missing the second half of the procedure. The server doesn't just send data, it also receives data too. How else do you explain how the server knows where each player is, who they damage and kill, and where they place in the scoreboard? The server HAS to get that info back for it to send that data to everyone else. Not only does the server have to manage to fill all the different cups and buckets, but it has to get water back, and then it takes that water and sends it to other buckets of other sizes, and obviously a small cup might have a little trouble keeping up with the servers demand.
Depending on how the game is coded to deal with this problem can determine if this even becomes an issue. Games like RO (and most recent games) are coded very efficiently and almost never have a problem. But other games (especially older ones) can let this lack of received data manifest itself, it could show up as the player "warping" across the battlefield, or having to aim very large distances ahead of a player to hit them, and some games will even slow themselves (and other players) down in a vain attempt to keep everyone on the same page.
Another player causing server lag may not be as commonplace today as it used to be (especially in RO), but it was never an "Old Wives Tale."