Hi Dometheus,
I did some research and some reading about the problem.
You may take a look at this links, if you like
support.google.com/mail/troubleshooter/2411000?hl=en
support.google.com/mail/answer/180707?hl=en
As far as I can see there is more than one factor involved if the message is thrown.
First it is the "Mail From" that causes the problem not the "Mail To".
If you use a gmail.com address as "Mail From" gmail will check, if the mail is really send from a gmail account and that is not true, because the mail is send from your server. Therefore gmail considers the mail a possible fake.
Second gmail uses Email authentication, which is a way to ensure that an email provider will be able to recognize the sender of an incoming message to fight spam and abuse. So even if a mail which is not truely send by gmail.com "claims" to be from gmail.com it can be accepted if it has proper authentification. There are different means of authentification and it is the mailers responsibility to make a proper authentification. So this would be the task of your provider because the mailder is located there.
Is it possible that your test system meets both factors?
Regards,
Aicha