Hey hey, a two month necro. Not bad for me!
Tom, if you're dealing with a Gmail account that's for an education institution, there's a default restriction for those domain to only accept e-mails from other Gmail authenticated/backed/validate domains. (I don't have access to the backend of such a system, so I do not know the exact technical language used to identify the term.)
I ran into this literally just now with a customer and came across your post while trying to figure out if anything can be done to make the receiving end OK with such e-mails. (Which if the case, could be a security issue so am happy I have not stumbled across such a workaround - yet.)
My understanding is there's a whitelist that can be used to allow e-mails from 'outside' domains to be received, but again without access to the receivers end, I don't know specific terms to be able to narrow down to a specific area.