No, you misunderstood. It's enough to protect you against random people sniffing wireless packets. Not other people that are on your network.
Are you suggesting that no generation of WEP or WPA protects against other authorized wireless users of the same AP, because they're "on your network"?
[rewritten completely to seek clarification]
If you have control over the internet between the AP and your server, then you're safe. If you don't, then how safe you are depends on how much you can trust the owner of each router along the way. In general, you should be okay, except that every now and then you might end up on an untrusted router, and it's then game over.