>> The lady's claim was (allegedly) that she has a perfect ability to distinguish between the tea-milk orders

I believe you added the word "perfect" which makes a substantive difference. I think this highlights the complications that get involved when trying to turn a simple proposition into an meaningful claim:

- Can we prove that person X can observe taste of tea with > 50% reliability with 95% confidence (what Fischer did)

- Can we prove that person X can observe taste of tea with 100% reliability with 95% confidence (not statistically possible)

- Can we prove that person X cannot observe taste of tea with > 50% reliability with 95% confidence (only possible if this person guesses wrong more often than randomly)

- Can we prove that person X cannot observe taste of tea with 100% reliability with 95% confidence (just need one example)