Bill
31977
I think there may be some confusion- Rolex 5512 is based on COSC movement. BUT!!!
We know this is Rolex and the are many experts who can justify one way or another.
It seems that there could have been different movements in the first (1959-1961) 5512 2 line which were capable cosc but what is confusing the issue here seems to be that the argument be made is that none of the 5512 2 line are cosc which is not completely accurate as the cosc is based on submitting for the certificate not exclusively based on a particular movement.
The 5513 was introduced as a non cosc watch to open up the market as a lesser priced watch. The 5512 never sold well due to the lesser expensive 5513 non cosc option.
I have heard and read that there are collectors with 2 line 5512 which have cosc papers. Below is an example image of a cosc for an early 66x,xxx serial which is around 1961. I am sure with a little more research you will find other examples of the cosc paper accompanying the 5512 2 line.
Bill