This is not true. Fannie Mae has outperformed the rest of the private sector in terms of loan performance (non-delinquencies). The organization also lost market share throughout the bubble to private sector lenders, not the other way around.
Your link provides no data supporting the contents of your post. There is a graph which ends in 2003, from which the blogger draws the same conclusion as you (Fannie has better non-delinquency rate). The graph does not show delinquencies at all, so I'm not sure where he is drawing this conclusion from.