One more time:

http://www.presidency.ucsb.edu/ws/?pid=72360

"Now, therefore, be it known that I, Andrew Johnson President of the United States, by virtue of the power and authority in me vested by the Constitution and in the name of the sovereign people of the United States, do hereby proclaim and declare unconditionally and without reservation, to all and to every person who, directly or indirectly, participated in the late insurrection or rebellion a full pardon and amnesty for the offense of treason against the United States or of adhering to their enemies during the late civil war, with restoration of all rights, privileges, and immunities under the Constitution and the laws which have been made in pursuance thereof."

"unconditionally and without reservation"

"with restoration of all rights, privileges, and immunities under the Constitution"

That means without conditions. "All rights and privileges" would not mean that you're mostly still a traitor.