The possibility to manually check/uncheck these checkboxes depends on the parametring of Ticket Type (for tickets), Activity Type (for Activities), Milestone Type (for Milestones), and so on...

On each type, you can specify for each checkbox whether it's locked or not.
If locked (which is the default) the checkbox is checked/unchecked only depending on the status.
It is a way to ensure that the checkboxes are conform to the workflow...

So, the administrator can easily change the behaviour of the checkboxes for each type, depending on the importance to respect a given workflow and/or the necessity to ensure the value of the checkboxes (for instance if they are used for some statistics).