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It's hard to imagine whether her route to discovering the truth is better or worse than those who didn't even know they were conceived through artificial insemination (the majority, because of Cline's advice to the parents). On the one hand, she didn't get the whole shock all at once and had some years of adjustment in between the two revelations; on the other, those psychological adjustments were based on false information and were at least shaken, if not destroyed.
The Guardian article isn't clear about this, but in fact a lot of these were cases where the parents had requested donor sperm. Jacoba Ballard, one of the main people quoted in the Guardian article, had been told she was conceived through donor inseminiation when she was 10.