The right to control one's own posts is a copyright issue. Posts to the group do not becomes the property of the group or group owner unless that member quits the group or otherwise disappears, essentially abandoning their posts. As long as the poster is a member, you can not take away that ownership, which is what disallowing deleting one's past posts would be.
Disallowing editing of one's posts is only allowed because the original poster (the copyright owner) still has the right to remove that post and optionally repost a corrected message or not.
Note that this does not apply to quoted text in other members' messages, however. Those are a reply to the original post, and such reference becomes part of the reply post.
Groups.io takes this seriously and egregious copyright violations can get a group shut down immediately, as that puts the entire groups.io system in legal jeopardy.
Dano
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Hi - have just changed our settings to read "not allow members to edit their messages" but it still allows members to delete past messages. Is this setting just working forwards in time and not backwards. If only forwards - then it appears a member can not only take out a message but also any photo attached/embedded.
Not so good in my view .........barry
D R Stinson