Geocaching Australia has never had the ability to delete logs by anyone other the log owner and the site administrators. The site administrators, on principal, don't get involved as any disagreement between cache owner and log owner soon spills over into a problem for the admin. We (the admins) are not interested in coming the meat in the argument sandwich. You're grown ups, you should be able to sort this through by discussing the situation.
We considered introducing this capability some years ago (June 2006). Here are some of the thoughts of the day which still hold true today.
as it goes against the open philosophy in some ways, and probably warrants community input
I like having the option to delete them. Another time I nicely asked someone to edit their log as they gave away too much.....
I suppose some people would just delete logs they didn't agree with.
Opinions of a cache would be subject to deletion.
Bad spelling would be subject to deletion.
"I don't like that finder" would be subject to deletion.
Spoilers would be subject to deletion.
Profanity would be subject to deletion.
"Get backs" would be subject to deletion.
"You did that to my find, I'll do it to yours."
Ultimately the community decided not to proceed with that and go with the idea that if you have a log that needs deleting, ask the log owner to take the action on their own log.
Regardless of that, this is a community site and as long as the principal of free and open is maintained, new discussions, changes, agreements and disagreements should take place and should a wide consensus arise, change will be made. So you have started the conversation, you need to encourage the discussion and see what arises.
Until then, you may need to contact the log owner and ask them to remove their logs and edit their spoiler.