If they use paid accounts I would expect them to strip info automatically. An "obvious" way to do that is to diff the output from two separate accounts on separate hardware connecting from separate regions. Streaming services commonly employ per-session randomized stenographic watermarks to thwart such tactics. Thus we should expect major publishers to do so as well.

At which point we still lack a satisfactory answer to the question. Just how is archive.today reliably bypassing paywalls on short notice? If it's via paid accounts you would expect they would burn accounts at an unsustainable rate.