***with influence based on personal insight***.

The phrase quoted by the asker applies ONLY to the "round" seated arrangement.

The writer contrasts the two seating arrangements, saying that:
- the "U" arrangement promotes dialog between the presenter and the participants
- the "round" one promotes dialog in a "team", where the presenter does not have more influence simply because of his position - he/She has an equal influence because a round arrangement gives none of the people an advantage. Thus, the only way to have more influence than another is through your knowledge, skill or "insight".

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Note added at 2 hrs (2007-05-23 12:41:19 GMT)
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Hmmm, after posting I re-read Bill's answer and realise I had originally misunderstood him - thus leading to my post. In reality, he says almost the same.