Nope I don’t think so. Parolee’s are still under the control of the State correctional department.
They just get to go home because they aren’t considered dangerous enough to keep in prison, but they still have not completed their debt to society.
Now I don’t think the police can go ransack their house looking for something, but I think they can stop by and take a visual look at any time.
Once probation/parole is over though I think they should have the same rights, including the unwritten right to privacy.
You are correct on all your points.