Perhaps the writer is confusing you because her omitted some of the words which form the parallel structure. at one of these [tables] sat the house-physician and at the other [table sat] the clerk... He is not saying "on one side of the main table sat X and on the other side sat Y" So, we cannot use "on" or "onto" because this would mean that the person sat on top of the table, which no one does.
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