This explanation is incomplete. Counterexample:
Amp pages are paywalled:
https://www.wsj.com/articles/freeze-or-cut-spending-fight-is... https://amp.wsj.com/articles/freeze-or-cut-spending-fight-is...
archive.is isn't: https://archive.md/LaiOX
Amp pages are paywalled:
https://www.wsj.com/articles/freeze-or-cut-spending-fight-is... https://amp.wsj.com/articles/freeze-or-cut-spending-fight-is...
archive.is isn't: https://archive.md/LaiOX
It might be using other techniques as well for bypassing paywalls, be it referer/user-agent spoofing (some old archives of sites that echo back HTTP request headers have archive.is sending a Referer of google.co.uk).