The problem with this argument is that it doesn't take into account how the non-public funded channels get their money. Most of them receive most of their money through advertising revenue, and the advertisers pay for their slots by increasing their prices. The net result is that if you buy pretty much anything you are contributing some small amount to the income of the TV channels that show adverts. This is also government enforced and as hard to avoid as the TV licence. In some ways it's even less fair as everyone pays it, not just those who have a TV.

The main problem the BBC has is that it's honest about how it gets its money rather than trying to hide it and thus takes a PR hit.