I see facilitating as helping people to learn. In order to do this initially a facilitator may have to "teach" so the group members or students are familiar with the tools they need to use in order to accomplish the learning.
Moderation to me is ensuring the learning is relevant to the purpose of the group or course (learning is focussed on the topic). A Facilitator needs to moderate the learning if it starts to go off at a tangent. In this course we need to meet certain criteria to pass. The Facilitator (Leigh) must ensure we do meet these criteria and so needs to do some moderating if we are not sticking to the topic.
Teaching is often thought of as giving all the information to students or group members so they just need to absorb it. I think a Facilitator at times "teaches" in a limited way: gives the student enough information to find the answer or solve the problem themselves in their own way & using tools they have chosen.
To sum it up a Facilitator has to be a Moderator & a Teacher at times.
When does the act of teaching compromise the role of a facilitator of an online community?
I think teaching compromises the role of a Facilitator when it takes over from facilitating, when the facilitator directs the group members to do something using a specific method because this is the method the Facilitator uses. Teaching is about opinions. A teacher provides information the way he/she sees it: their point of view, there are no options.