Yes it is true they that you are not allowed on the island. It is a nature reserve / conservation area of some sort. There are usually only 3 people living (semi-permanently) on the island who maintain the lighthouse, I did not see them this time, but I have chatted to them on the island a few years back.
It is best to get into contact with the lighthouse keeper if you want to arrange to go ashore.
I have dived for crayfish there a few years back and was not aware of any sharks in the area. Just did some googling now and found it is apparently quite a sharky area