I've found a way to exploit the Fate system such that you do not need to Level Sync in order to gain credit for participation.

The exploit works as thus:
Equip any buff or healing skill (class/job does not matter).
Approach a fate, but do not level sync.
Use the buffs (heals work best) on other players who are participating in the fate.

When the fate ends, you will receive rewards as usual based upon contribution even though you were not Level Synced.

It is possible to receive Bronze, Silver, or Gold by using this exploit.