No. This is a very old debate I'm bringing up. The criteria for being listed as an "infected site" is not clear enough.
If I’m about to enter my credit card information on a site that’s compromised, I don’t care if it’s because of infected first party code or infected third party code. I want my browser to say “bro this site is fishy, maybe don’t”.
Your example is how the site got infected. The types of infection is listed 2 or so paragraphs above that