Destiny gets super weird when you start lagging out
Destiny brings players together from all over the world. It's not always a good thing.
Destiny, like any online multiplayer game, attempts to compensate when players hit lag spikes or other Internet issues. Unfortunately, it doesn't always work.
YouTuber AfroToast blames the weirdness in the video below on Australian infrastructure, as we are wont to do, but anybody with a poor connection is likely to see bizarre phenomena of this kind. Unless you can guarantee your upload speed and that of your opponents, and ensure you're reasonably close to each other geographically, this sort of stuff can happen even when you connect via dedicated servers - let alone peer-to-peer hosting.
At least these netcode fumblings are more entertaining than just always missing, or dying as soon as you spawn.