The object attributes that the UI describes as "Share with Group" (which enables anyone in the group that the object is set to to manipulate the object in various ways) is pretty much entirely different from the action that the UI calls "Deed to Group" (which changes the owner of the object to the group, and allows group members to manipulate the object as specified in the group's settings).
The one place where these two things are linked is in the fact that before an object can be deeded to a group, it must first be shared with the group. This has resulted in various things that are deeded to groups for land-mangement purposes (radios and TVs and other media controllers on group-owned rental land, for instance) ending up also shared with the group more or less by accident, which has various negative consequences (in particular, other renters in the same group can manipulate those objects in various ways, and cause trouble through malice or ignorance or carelessness or simple error).
This JIRA item proposes fixing this design bug by removing the requirement that an object be shared before it can be deeded. This change would break no existing content, or even existing habits; the only change in behavior would be in the case where someone attempts to deed something of theirs to a group without first sharing it. After the change, this would succeed, rather than failing.
(As a separate change, it might also be useful to decouple these two things visually in the UI; but that would be a different JIRA I think.)
CLARIFICATION: The suggestion here is that Residents be able to deed their own objects to a group without first sharing them with the group. I don't intend to suggest that anyone be able to deed random objects belonging to other people.
I've edited the wording above to make this clearer. Thanks to Prokofy Neva for pointing out the possible misinterpretation.
That said, accidentally deeding an object can be tragic. If the object isn't transferable, once deeded it's lost if it's returned. If an object isn't set permissive for the next owner, a build can accidentally be made no-mod and no-copy. The current two-step workflow prevents accidental clicks. Even if this changes, it would be good to maintain some form of protection here.