At the LSE, PhD students don't teach. By teaching, I Mean they don't conduct LECTURES. What they do , is they act as tutors, and discuss case studies, and other material.
Seriously, why make such a hue and cry. Some if not all of the PhD students at LSE, publish research of repute.
You simply need to be there, to understand why it has been regarded, and is still regarded in awe, particularly in the social sciences.
It is awesome for a reason, and that reason is that is it well ahead of other universities, particularly in the social sciences.
It's a pity that Ringmar didn't mention that fact or emphasize it too much.