FWIW, I agree with you that saying she couldn't have done it because she has black friends is silly. She definitely could have done it out of ignorance.
It's worth pointing out that Australia has a very small population of African/African-descended people, and most moved here within the last 10-15 years. I'm around the same age as Dianne, and when I was a kid I could have counted on the fingers of one hand the number of black people I'd ever seen in my life. Seen, like for 2 seconds on the street, not met. The word would not have anything approaching the same amount of impact here as in the UK or especially America. Obviously we all know it's bad, and not to say it, but quite a lot of people probably wouldn't think much of singing it in a song unless specifically told not to.
I remember in middle school, people awkwardly asking POC classmates if it was OK to sing, and them shrugging and saying they thought it was probably alright. Obviously, massive cringe to look back at the ridiculous image of a bunch of white kids nodding sagely as South-East Asian and Pacific Islander kids tell us the n-word is probably ok for us to say so long as it's in a song.
If she did do it, it could simply have been force of habit she hadn't broken yet. She comes from a way smaller town than I do, so it's very likely she also had never met a black person until she was an adult.