Fusarium Disease in Basil: Is It a Concern for Other Nearby Plants?

I was curious, after reading your info sheet, if the Fusarium fungus is a concern or problem for any other plants or herbs (outside of the mint family) growing in proximity to basil that has been infected?

The fungus disease that attacks basil, Fusarium oxysporum, comes in species specific races. As mentioned in the Richters InfoSheet on fusarium, the one that attacks basil, Fusarium oxysporum forma specialis basilicum, is capable of infecting other commonly-grown members of the mint family to which basil belongs without noticeable symptoms in the host plants. While there is no apparent damage to the host plants, the problem is that the fungus can jump from an asymptomatic host plant to basil and cause death.
Can this race attack other plant species outside basil's family, the Lamiaceae? There is no evidence of that it can, but I am not sure that this question has been adequately studied by researchers. I would put it like this: it is unlikely that it attacks species outside the mint family, but it can't be completely ruled out at this time.
For more information on fusarium disease (including a list of the different types) see the University of Hawaii's "Fusarium Primer":
https://www.extento.hawaii.edu/kbase/Crop/Type/fus_prim.htm