Proposition: Finite samples do not recover every source weight exactly

At any fixed finite $n$, no classical inference procedure on the complete word list returns the exact value of $\theta$ with probability one for every $\theta \in [0,1]$.

Proof. Under the calibration assumptions every one-shot outcome has strictly positive probability for every $\theta \in [0,1]$. Hence every finite word list has positive probability under every such $\theta$.

Suppose a possibly randomized inference procedure returned ${\theta }_0$ almost surely when the parameter was ${\theta }_0$. For each word list its conditional output law would then have to be concentrated at ${\theta }_0$, since each list has positive probability. The same conditional output laws are used at any different parameter ${\theta }_1$, so the procedure would still return ${\theta }_0$ almost surely. It cannot also return ${\theta }_1$ almost surely.