medical test result - can we find a better answer than M. vos Savant?

[Arnold Winkelried]

Here is the Q&A from Marilyn vos Savant's Parade column yesterday (I am paraphrasing)

Question: I have a 50% probability of inhering a certain gene. I can be tested to find out if I have inherited that gene. If the test shows I have the gene, I don't want to know. On the other hand, if the test shows that I do not have the gene, then I want to know. Any suggestions?

Marilyn vos Savant answers:
Take the test. Afterwards, the doctor flips a coin. If the coin flip results in tails and the test showed that you did not have the gene, you are told that you do not have the gene. Otherwise the doctor tells you nothing.

You can ask the doctor to flip the coin many times, with the same rules.

If the test shows you did not have the gene, you will probably eventually know. If the test shows that you did have the gene, you will never know for sure.

I think her answer is not very good. You will never know one way or the other, you will just "probably" know the answer.

On the other hand, I think there is no solution to the problem as stated.

Any better ideas?