Answer

Very interesting. Of course it immediately brings to mind the Roy Meadow case in Britain, which I use to illustrate this issue (Munchausen by proxy).
But here, specifically, it seems that this was not a statistical error in the same way as there. After all, here there was evidence from the diaries; four infants is not like two (the probability here of independent accidental death really is tiny, far less than with two). There were also her statements (she practiced her version for court), and so on. Therefore, probabilistically there may indeed have been a proper basis for suspicion here. What changed things were the new scientific findings, which show that there were medical reasons for the deaths, and that changes the picture.
It seems to me that unlike Roy Meadow, where there was also an error in the reasoning itself, the only error here on the statistical plane was ignoring the assumption that there could be a connection/dependence between the cases (such as a genetic connection). In other words, these were not independent cases, and therefore the probability of their occurrence is not the product of the probabilities. That error was also present with Meadow, but as noted, in his case there were additional errors (accidental crib death of two children is a probability that is possible if you examine it across all mothers in Britain or the world. Four already really is not).
By the way, although she did sit in prison on the basis of a mistaken interpretation (or lack of scientific information), even now there is no certainty that she did not murder them. The probability of that becomes such that conviction is no longer possible (not beyond a reasonable doubt). Still, I do not think the suspicion against her is negligible.