It's a pretty massive stretch to go from "ISPs are permitted to block illegal traffic" to "ISPs are required to perform deep-packet inspection to ensure the legality of all traffic they carry".
If you've got a huge wallet you could run your own physical infrastructure but it would be hugely expensive for anything more than a small userbase [1]. If you went that way you'd make peering agreements with your closest internet backbone providers to hook into the rest of the internet (backbone providers being even bigger ISPs than those mentioned earlier, the ISP's ISP if you like)
[1] It has been done in the past: http://www.techradar.com/news/internet/how-to-start-your-own...
On the other hand, besides the ACLU and maybe a few people organizing over the internet, there will be no money spent in lobbying to tighten up definitions and improve privacy.
So there, it's a 'pretty massive stretch' but by no means it's an unexpected thing.
Also, they both require the same technology to be automated and possible. The main constraint for the latter is computational power.
Yet that regulation cannot exist without this Right.
And the regulation is required to limit the abuse this Right can bestow on users.
This is a tricky one, because the right and the law are both mutually exclusive and mutually inclusive.