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The documentation for the methods in statsmodels.stats.contingency_tables.Table is sparse; for example, for fittedvalues() it describes it "returns fitted cell counts under independence". What does it fit each value to? The additional information says the returned cell counts are estimates under a model, but what model?

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The fitted values are the estimated mean cell counts under the independence model.

If p1 + p2 + ... = 1 are the row probabilities, and q1 + q2 + ... = 1 are the column probabilities, and N is the total sample size in the table, then N * pi * qj is the fitted value for cell i,j of the table under independence.

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