I am saying HC that have picked their GMs usually have roster control. Shanny for example has roster control in San Fran. Lynch cannot make a move that Shanny disapproves of. It is in his contract.
Jim Harbaugh was hired first and basically chose his GM who was an exec with his brother's team. He has final roster control
New Chargers head coach Jim Harbaugh will have the opportunity to make key personnel moves for the franchise
clutchpoints.com
So again I cant really think of any example where a HC essentially picks his GM but doesnt have final say on the roster.
Once you give the HC power to decided his GM then you are telling the HC they are more important than the GM. So typically they want that embedded in their contract by being given full roster control. The GM then just becomes the guy that does all the legal work for them but the HC makes the final decision.