Contact Form 7 with embedded IS webform optin

I have someone that has the CF7 plugin enabled and is trying to get an embedded IS webform for optin to work on their site. The embedded webform won’t submit. When I look at the source for the resulting page it appears that both the webform and cf7 elements are getting referenced (possibly causing a conflict?).

Does anyone know if there is a known conflict with cf7 and embedded webforms? I’ll tell them to try dis-abling the plugin but thought I’d ask if anything was known about it first.