I don’t doubt that she said it, nor do I doubt that she intended that, but the text doesn’t support it. What Hagrid said actually contradicts it, though he’s admittedly an unreliable narrator. The only other time I can find where it’s mentioned in the book is in Harry’s confrontation with Voldemort at the end, and all Voldy says about it is: “…but your mother needn’t have died…she was trying to protect you…”
I’d call it a slip. Either she intended Hagrid’s narrative to establish it, but didn’t quite write it that way, or her memory of it was a bit fuzzy during the interview, and she conflated something she intended with something she actually wrote. After all, the interview took place ten years after the book was published, and I doubt she’s re-read it as often as many of her fans; it would be easy enough to mix up several draft versions of those lines with the published one after that much time. It doesn’t really matter to the story, either way. The Potters had defied Voldemort enough to make themselves a target; they were members of the Order, after all. They had established themselves as his enemies sufficiently without a specific rejection.
I’m sure he would have been pleased to have them on his side–psychopath that he was, all that would have mattered was that they were useful to him–but that clearly wasn’t in the cards. Since they weren’t going to be useful to him, and they were in his way, he killed them. My interpretation is that he only offered to spare Lily because she would have given him another hold on Snape; she was just another string to tie onto one of his puppets.