Interesting. I kind of don't understand why it would make a difference in this particular case. Let me explain that it is "a legitimate certificate for my domain". I can see my certificate and I got to that server thru the IP address.
I'm more than happy to fix it but I'm not paying $100 for a server license or $500 a year for something or another that seemingly doesn't offer any better security. Requiring that these solutions take more than a button push or two from "the average developer" indicates (to me) that something is slightly wrong with the way security currently works.
It is not necessarily my server if I see my own certificate in the warning?