Cigarettes aren't banned. That doesn't mean everyone gets free cigarettes.
I can't stop you from going online but I don't have to give you a computer to access it?
Again what's the difference? Your actions forbade someone from using the internet, what's the difference besides playing dumb word games?
You can get some money together, go and buy a laptop, connect to free public wifi. The government cannot ban you from using it if you complete those steps. i.e. they cannot be the only thing preventing you from accessing the internet. If you have no money or no way of buying a computer or no way of accessing a connection that's on you, the government isn't required to give you those things for free. Huge difference between the two concepts and very much not word games.
I'm pretty sure US prisons don't allow you to have a laptop (they certainly don't permit cell phones), nor is there likely to be public wifi on the premises.
I'm not sure how you can't see the difference. If you have a laptop + Internet subscription you can access the internet. If you don't, tough luck.
"Access to the Internet" is the right. Not the tools to access the internet.