Medicare Part D plans are run by private insurers and 
  they certainly do negotiate on price.

Why is a third party negotiating for Medicare, rather than Medicare negotiating directly? Because they're smaller, and have less leverage.

  physician administered drugs are paid for at a rate 
  that is the average of what private payers pay.

Why is a third party negotiating for Medicare, rather than Medicare negotiating directly? Because they're smaller, and have less leverage.

From http://www.cnn.com/2015/09/28/health/us-pays-more-for-drugs/

-- Gleevec (a cancer treatment): $6,214 (per month/per customer) in the United States, compared to $1,141 in Canada and $2,697 in England.

-- Humira (for rheumatoid arthritis): $2,246 in the United States, compared to $881 in Switzerland and $1,102 in England.

-- Cymbalta (for depression): $194 in the United States, compared to $46 in England and $52 in the Netherlands. In fact, there is also a generic version of Cymbalta so these prices reflect having a cheaper alternative.

Some molecule. Different price.