There's a substantial difference between being trained and being overfit to repeat training data 1:1. Overtraining is a bug of a model, not a feature. For example, Stable Diffusion 1.4 is overtrained on one specific Aivazovsky painting (among some others by other authors, like Mona Lisa, or Sunflowers - Van Gogh painted several of those). Copilot was famously overtrained on Carmack's fast square root code, so they had to block it programmatically after receiving bad publicity. Both are not intended by model authors, this is a flaw.