You are right-Lincoln did coopt the AP, but the change was broader (obviously, the Confederate news services were doing it too).
Not only so, but southern states had been restricting the deployment of telegraph lines long before the Civil War. There simply weren't that many telegraph lines in the South. Hardly any, compared to the North.
I haven’t seen these #s, but it would be interesting to find out the total # of telegraph miles in the U.S. in 1860.