We think her Dad has never said that and that's just what she tells DS.
You're quite right, you cannot trust a single word that comes out of her mouth. She'll lie even when there's no need to.
I hate to say this, but your son is also not covering himself in any glory here - being angry at you for those messages, you what the hell is his justification for that?? I hope he's pulled her up on that?
He is the victim in an abusive relationship. It's not a normal relationship, his head is full of confusion - he won't know which way is up. The GF is manipulating him, and anyone else she can, to get her own way, which will never be enough. If OP had said she wasn't going to see her son for his birthday, GF could have it all, it still wouldn't have suited her. She will always be fighting against everyone, she will always be the victim, in her head.
The OP's son has to keep himself safe (although he'll not realise that's what he's doing at this stage, it's happening subconsciously) and if that means blaming his mum, that's what he will do. Also because he knows he is safe with his mum, if he was to stand up to the GF he would be severely punished by her - but DS was near hysterical telling him not to as it just makes things worse.