Nessa, it's so hard when kids say things like this. Their perception of things is so different from ours. Maybe when she does get a smack, tell her why in no uncertain term. T he only thing I could think of is tell her exatly what she did wrong and that a smack is the consequence, every time she gets a smack. You might already do it...
I think one thing you night need to be aware of though is that at her day care, even though her carer said they don't really take much notice of it, probably since they know your family fairly well, there may be other carers who do, like a casual worker, or a student teacher. I am a childcare worker and the first instinct in me when a kid says anything along the lines of what she is telling people is to document it. It is also a childcare worker's responsibility to report any kind of suspected mistreatment of children in thier care. . If she says it a few times to the same person ,then that would be grounds for them to report. Even if she said it to another parent at her childcare centre. Maybe if she got the attention she might be suseptible to embellishing a little if they react the right way for her. We are also not really allowed to question children if they say anything like this to us. So if they are doing it the 'right' way then a chidcare worker can only make non-leading comments then document and take further notice of the child and any other comments they might make.
This is a tricky situation for you. She is old enought to realise the consequences of actions, so telling her why she got a smack is probably the only way to get her to understand. Maybe even if you tell her that it makes you/daddy feel sad/ hurt when she tells people that he hurts her, because they can think the wrong thing about him. I dont know!!!
Good luck.