Bhagavad Gita, Chapter 18, Verse 16

Such being the case, he who through a non-purified understanding looks upon his Self, the Absolute, as the agent, he of perverted mind sees not.

Believing the soul alone did something is named here directly as a real, specific error, not harmless simplification.

Krishna calls this belief a mark of impure intellect, not just an innocent oversight. Real clarity means seeing all five factors at work, not crediting just one.