Synthetic data doesn't require using another ML models output as training data. One incredibly successful way of generating useful synthetic data is using rules

Synthetic data doesn't require using another ML models output as training data. One incredibly successful way of generating useful synthetic data is using rules. For example, AlphaZero uses synthetic data (playing against other versions of itself) but it does gain information because the data is generated against the rules of the game. Similarly, word2vec and other vector representations use synthetic training data, but that data is derived from observations of text (no, it's not using raw text, each training instance is generated from the text, with varying levels of simplicity of course). Tesseract is trained using synthetic data generated from font files and simulated "rendering errors." Synthetic data should not be underestimated.