I am learning about Fisher Consistency and came across this section of a Wikipedia article (https://en.wikipedia.org/wiki/Fisher_consistency#Relationship_to_asymptotic_consistency_and_unbiasedness) which gives the following example of "Fisher consistent but not asymptotically consistent":
Take a sequence of Fisher consistent estimators $S_n$, then define $T_n = S_n$ for $n < n_0$, and $T_n = S_{n_0}$ for all $n ≥n_0$. This estimator is Fisher consistent for all n, but not asymptotically consistent. A concrete example of this construction would be estimating the population mean as X1 regardless of the sample size.
I see how using $X_1$ as the population mean estimator is not asymptotically consistent, but why is it Fisher Consistent?
The loose definition of Fisher Consistent from the same Wikipedia article is "if the estimator were calculated using the entire population rather than a sample, the true value of the estimated parameter would be obtained", and I don't see how $X_1$ achieves this.