This is a classic example of: "Assume a spherical cow". The game is also about hand/eye coordination, as well as solvability. So given the helpful precis:

"Summary: it is possible to play Tetris and guarantee that you will score at least one line, no matter which pieces are given to you, i.e., even assuming they are chosen adversarially."

We can confidently respond: "bollocks".

Great write up and analysis.