Well in theory the government is the public, as the public elects the government, as Canadian happens to be a Parliamentary Democracy. As it stands right now, the government has no control over the CBC and the public have not given it a mandate to do so. The funds go directly from public tax to the CBC. It would not be possible for the government of Canada to currently unilaterally make that change. If they did, I think it would be fair to change the label to a governmental media organization vs a public media organization. We would also presumably want to change calling Canada a democracy.