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A frequentist interpretation of inference assumes parameters have fixed, but unknown values. In this paradigm, it is sensible to speak of the statement "this parameter's value is zero" as either true or false.

I do not think it is accurate to portray the author as someone who does not understand asymptotic statistics.

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> it is sensible to speak of the statement "this parameter's value is zero" as either true or false.

Nope. The correct way is rather something like "the measurements/polls/statistics x ± ε are consistent with this parameter's true value to be zero", where x is your measured value and ε is some measurement error, accuracy or statistical deviation. x will never really be zero, but zero can be within an interval [x - ε; x + ε].

As you yourself point out, a consistent estimator of a parameter converges to that parameter's value in the infinite sample limit. That limit is zero or it's not.

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