Look at the list of insignia for O6 here. Three of the four look to the right, but the Navy one looks to the left. Why?
There are two eagles worn on the collar. One faces one way and the other the other way. For some reason the web-site you linked to chose to show the other insignia for the navy.
The American O-6 (Colonel/Captain) rank is the only officer’s rank that is directional, in that the eagle looks forward–similar to how the American flag looks ‘reversed’ when worn on Army uniforms (supposed to be leading forward, as in the flag is fluttering behind the forward-moving staff).
For some reason, that particular page doesn’t really show that or explain it well. I think it has to do with the other graphics: the shoulderboards and sleeve stripes.
Just an oversight, IMHO.
Tripler
That page was probably put together by some underpaid civilian. 
Just to clarify, this is the case for all of the branches (Army, Air Force, Navy, Marines, Coast Guard) when uniforms with insignia are worn.
The only exceptional thing about the Navy (and Coast Guard) is that their are some uniforms in which striped sleeves or shoulder boards are worn instead of the insignia.
Thanks, guys!
Substitute “there” for “their.”
(I hate it when I do that!)