IceBear has a flexible permissions system that lets you control who can - and cannot - see and change items.
In short:
Users may be given additional permissions under certain circumstances.
A project owner is the only person (except administrators) who can create and modify proteins within the project, grant and revoke usergroups' permissions, and change the project owner.
For more details, see the project help.
A plate owner can always see a plate and set its protein, regardless of their own permissions. Plates are imported into a default project, where nobody has any permissions, therefore the plate owner is the only one who can see the plate until it is assigned to a real working project.
For more details, see the plate help.