The replication wizard, when used in basic mode, does not set the destination dataset to read-only by default.
Once the task is set up, it's necessary to edit the replication task and change the destination set read-only policy from IGNORE to SET.
If the User Guide is to be believed, opting out rather than opting in to read-only is the correct behaviour. This makes sense as you don't want the replicated dataset writeable by default.
Refer to this forum thread for more information