When in the users tab, "update ownership" indicates when a process is "In Progress" but it does not indicate if a process is "Unpublished" and is not ready to be published. The way to differentiate status is in the Process list report but it should be indicated on the "Update Ownership screen. It could be the same blue warning as for "In Progress".
When transferring ownership from this page if the process is Unpublished there will be no blue triangle warning, as after transfer the process is only increased by 0.1 so it is not published. Published and In progress processes will be published using this transfer method however.