I doubt it has anything to do with Twitter. I would say that those are those "friend links" (or how they are called). You can link to your Medium article via a special link that bypasses the paywall. It's a Medium feature. I would guess that Twitter sharing uses that kind of link by default (who knows for how long).

As for browser add-ons, I have my doubts. The solution Medium implemented seems pretty solid. Also, there are already "services" that try to get around paywalls by accessing archived web sites, but it does not work on fresh Medium articles when the discussion happens.

Frankly, while people eagerly lock their articles, billionaires, and greed in general, already won.