A few things should be noted about this. Did you ever check the time of when that conversation took place? April 17. About a week before the moderators for Health SE were appointed. Also, the same day that Shog9 made a meta post for some spring cleaning. In the meta post, he specifically says
- Flag answers that consist entirely of links / quotes / or references without bringing any knowledge or expertise to relate them to the question. It's awesome to draw heavily from (trusted) sources, but be sure to pull out the key relevant parts and tie them back to the specific question at hand.
JohnP and I were discussing this, and we were flagging quote-only answers for moderator attention, before there were any moderators appointed here. The deletion of these answers wasn't decided by us, though we did flag the answers because we were asked to by King Shog.
Now onto your question: Should deletions of answers be decided by moderators only?
Right now, moderators are the only people who can delete answers. When we get more users that have 4k rep, which is needed to vote to delete an answer, then this policy will change. Right now, it is up to us to delete answers, but there are some things we will try to do before we delete them. Though I will admit that we did delete a lot of answers that were quote-only, or broke some of the other guidelines set by Shog, but now, we are trying to guide the answerer to improve their post. We will delete though, if the answerer refuses to improve or if the information can be dangerous.