You do have to cross the rope bridge to get the quest to complete properly. I tried to swim to the island and recieved the discovery reward, but you MUST take the bridges to complete this portion of the quest.
just did this, after 20 minutes of sneaking round the island and being chased by nasty skels i finally got the tick as i ran from the tomb of varsoon towards the rope bridge. About 5 metres (if u can imagine that distance)before i started to cross the bridge.
Had problems with the forbidden isle, with all the undead around, i swam onto the isle and got the tag that i was there, but i still didnt get the location compleete, not sure, but ive heard that you have to run over the bridge to get the compleete quest, its not enaugh to go onto the isle itself. *cannot confirm this yet though.