There are many myths.
"The likes of Netflix, Amazon etc pay for their internet connections and content delivery."
True. Netflix and Amazon pay say, Level3. Not your ISP. If your ISP doesn't peer with Level3, they have to pay Level3 for transit to get to Netflix or Amazon. Level3 gets paid twice, so the transit providers are really the ones double-dipping. As your Netflix subscription means increased transit traffic, your subscription effectively becomes an increased cost to your ISP, reducing the margin they make on your connection. Which is usually very small already.
This is also where potential clobbering comes in. Netflix and Amazon being kinda huge almost certainly pay less per Mbps for transit vs a smaller content provider or small ISP. So one side of the deal connection Level3 may charge 10-20c/Mbps, the other €1-2 for the same bits. So this is relatively normal, ie buy in bulk, get better pricing. But it's also where regulators tend to (or should) take a closer look to see if there's SMP (Significant Market Power) and any market abuse or competition concerns.
"They pay to deliver the data to the public exchange, the ISP pays to take it from there to their private network (which is what their customers pay them to do). Netflix is open and upfront about this. It says on their web site, in black and white, that they will only engage in private peering in limited circumstances."
But that approach can be bad for both quality and cost. It potentially keeps costs down for Netflix, but may force additional costs onto the ISP. So where Netflix is present on an exchange, they rent a few ports and can peer with multiple ISPs. The ISP does the same, but if Netflix traffic exceeds their port capacity, quality drops and they'd be forced to pay the exchange for additional ports. And to borrow from another commentor- "LINX applies a surcharge if your ports exceed 80% of capacity, that's all". Generally if you're exchanging substantial traffic with another peer, it's better to take that off-exchange via private peering. But that would mean Netflix would have to have more ports available, so again they're avoiding costs and passing them through to the ISP.
There are also other potential challenges, like Hungary's proposed Internet Tax. If that happens, ISP's would get charged a per Gbps tax for your video streams. How would that cost be recovered?