i think it all depends on the private institue's teaching and learning quality . If a certain institute has built a good quality reputation over the years,its diplomas will not only be recognizable but sought after.It is true though that private schools are required to do more than average just to prove their reliability . But online or offline independent home study is no more solely exclusive to the private sector.I noticed that the government of ontario has implemented a good policy in boosting the image and reliability of private learning programs by entering into partnerships with colleges and universities
check this ontario elearning program for example