Answer / Justification:
Is naturalized or occurs as a casual in some countries of Europe (Great Britain, Germany and Switzerland) (Centaurea diluta Aiton, new to the Italian flora). These countries do not overlap by more than 50% with California's climate zones (Cal-IPC global map of climate areas matching California).
Per Reviewer Lynn Sweet: The problem with evaluating this species is that it is listed as "noxious" on the FAO list for "agricultural areas" in Spain, where it is "native." The only areas that I can figure out that it is possibly documented to be non-native and invasive are a) Hungary http://www.cabi.org/isc/abstract/19922318884 and Malta (cited source, Schembri and Lanfranco). ITIS mostly shows this to be a casual alien in many places, with vague "weed" status in the US http://www.hear.org/gcw/species/centaurea_diluta/ . Otherwise it seems to be just in disturbed areas or in agricultural areas (which are important for this question, but whether this is happening in its non-native range seems to be a question) or very rare casual in Great Britain https://www.brc.ac.uk/plantatlas/index.php?q=plant/centaurea-diluta.
Screener response: Q2 is related to naturalization; Q4 is related to invasiveness (causing economic damage, etc.). Naturalization does not confer automatic invasiveness. That said, something causing major economic damage as an agricultural weed, as this is, would be considered invasive, regardless of whether or not naturalization has occurred.
That said, Q2 should still be a "Yes", because new protocols regarding climate matching indicate that ANY match in climate with California makes this a yes; as Switzerland and Germany overlap with California's climate zones, this becomes a "yes".
More information from Lynn Sweet: The text is misleading, sounding as if this species has naturalized primarily in temperate climates. The species is noted as native to Southwestern Europe and North Africa. It has become naturalized, according to the source listed, as in Great Britain, and "central Europe" (the cities listed in the one source are in Germany and Switzerland) as well as in Italy, Malta and Hungary. Looking at the "Cal-IPC global map of climate areas matching California" this distribution differs slightly from areas matching CA, with some of these naturalized occurences seeming to be in more temperate areas. On this, I suspect a) propagule pressure since it is a noted bird seed contaminant https://www.brc.ac.uk/plantatlas/index.php?q=plant/centaurea-diluta, b) microclimates such as southern-facing slopes or exposure-buffered areas or c) misidentifications with the similar C. maculosa or C. diffusa, which is noted in Flora of Missouri entry: http://www.tropicos.org/name/2702146?projectid=23). On this issue, while other sources agree on taxonomy it seems, GBIF has a really confusing taxonomy for this species, so it's hard to know which observations to use from that source.
So I'd suggest add Italy and Malta to the text. I just think there is some ambiguity as to whether it is extensively naturalized in these temperate areas at all, and it does seem to be naturalized in areas that are similar to California, including 53 specimen records from coastal California.
Screener response: this remains as a "Yes".