There are endless debates within CNF about the boundary zone between fact and fiction -- but for me, I am fine with a writer using imagination so long as they cue the reader that they are using imagination (i.e. "I imagine that my mother said such and such to my father, but perhaps there was nothing but silence..." (a garbage line, but you know what I mean...).
I think a creative non-fiction writer can use all of the tools available to a fiction writer, so long as they let their reader know (that's what I mean about "maintain the contract with the reader to tell the truth). And, if they don't, they are probably just writing straight non-fiction (think traditional journalism).
So, the 'creative' aspect of creative non-fiction is really just in the method used to tell the story (for instance, maybe a collage style written in snippets or maybe incorporating allusion and metaphor) but it does not mean being "creative" with the truth (i.e. making things up for the sake of making things up).
There should not be a dilemma about accuracy -- if the writer finds themselves there, they are likely writing fiction based on fact, and not telling a true story and they need to package it as such.