As quoting from the post, "TIL as part of pre-Columbian Aztec child sacrifices, children were required to cry so their tears would wet the earth to appease the Aztec deity; if they didn't cry, priests would tear out their fingernails before the sacrifice to trigger crying."
Like you, I have read the allegation in secondary source texts. It is absolutely certain that the Aztecs practised child sacrifices, as this is proven both by archaeological discoveries and by the primary sources. However, it is much harder to substantiate the notion that priests tortured the children to cause then to cry. To be clear, crying was considered a good omen. Yet, I cannot find any clear reference in the Florentine Codex (Book 2: The Ceremonies) to priest pulling the children's fingernails. The Codex gives the impression that tears were desirable, but not that they were deliberately induced.
I also checked Durán's Book of Gods and Rites. A salacious detail like the tearing of fingernails would fit with Durán's sometimes exaggerated accounts. But I can't find a clear reference to this here either. Now, it is possible that I overlooked the detail. Alternatively, it may be in another text such as Torquemada's Monarquia Indiana, or Motolinia's Historia (which unfortunately I cannot check as I do not have them in my possession). However, if the detail was in these text's I'd be cautious. Motalinia was much less rigorous than either Sahagún or Durán, and Torquemada wrote considerably later than either of them.
I don't know if this really answers your question. But I'd be a little cautious with the allegation until I could find a direct description in either Sahagún's or Durán's accounts.
Sources: Sahagún, Bernardino de, General History of the things of New Spain Book 2: The Ceremonies, tr. by Arthur O.J. Anderson O.J., and Charles E. Dibble, (Santa Fe: University of Utah, 1979)
Durán, Diego, Book of the Gods and Rites and The Ancient Calendar, tr. Fernando Horcasitas, and Doris Heyden, (Norman: University of Oklahoma Press, 1970)