Spud - We certainly don't mean to patronise you, and I am sorry if that is how you feel. However, you need to realise that people use this forum in order to share knowledge and experience, and we are just trying to help you.
It is a simple FACT that people who work for the Home Office and for UK Visas sometimes give the wrong advice. I have a number of cases on my desk where this has happened, and Garry has about a dozen complaints against people who have misadvised. It would be nice to accept all that these people say is right because it comes from the horses mouth, but that is, alas, not possible. Just because the guy you spoke to said it sounds okay, it doesn't mean that the man in the Embassy who actually looks at the paperwork will make the same decision.
Although I appreciate that the father of the child has never been granted anything in terms of custody, and has been absent from his life, this may not be enough if your girlfriend does not have formal custody. It may be that it is, but I would err on the side of caution, and get some kind of order. The ECO will not simply accept your girlfriends word for it anyway - they would need evidence.
Victoria