This is doubly misleading. A lot of private data is sourced through providers like e.g. Mercor, who pay experts to answer questions and write out their reasoning. (E.g. paying a software engineer to write a project from scratch and recording every keystroke, paying a Chem PhD to answer hard Chem questions, etc.). A second source of private data comes from custom RL environments with fine-grained intermediate rewards for e.g. software engineering, financial modeling, etc.. Also, imagine the amount of usage data recorded by Claude Code, etc.
Pretraining is mostly curated public data, post-training is increasingly private expert data and tests.
Well since you work at a lab you should know that most capabilities arise in pretraining, not posttraining or mid training, and the latter two mostly function to bring out the hidden intelligence in these models more than anything else.
Source: Work at a lab, common knowledge.