"...I simply can't understand why she just doesn't admit the errors that the NCCL made, admittedly made before she was involved with them." [My italics]
Surely there's the answer. It was nothing to do with her. Why should she apologise or admits that mistakes were made before her arrival at the NCCL? Strange that the Daily Mail should kick up a fuss. If, God forbid, I should become a politician, and the DM ran a story along the lines of "jim360 connected with Cambridge Spy Ring"... I'd be inclined to answer the question, "But will you admit that communism was a failed vision and that undermining the system from within was a traitorous act that helped no-one?" with "Oh bugger off, it was nothing to do with me. Go and do some proper journalism."
A bit of an extreme example, perhaps, but there are surely some parallels.
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That said, the Today Programme reports that a spokesman on her behalf has said that she "regrets any connection between [the NCCL and the PIE]" but that such connections were "Immaterial" to her work.