Actually it does because it is upon that logical fallacy that the counter argument is entirely built upon. In a general way, a logical fallacy would not imply that he was wrong if it was simply acessory or lateral to the issue. Correct me if I am wrong, please.

A ⊢ B is invalid (without any other premises) but proves nothing about the value of B.

Indeed even if we have

A → B, A ⊢ B and can show that the initial premise is false (which reduces then to the above) we still can't say that the assertion of B [being true] is incorrect only that the logic is unsound.

In traditional style:

All men are Greek, Aristotle is a man ∴ Aristotle is Greek

Despite the premise being provably false (under ordinary interpretation), thus the argument being unsound, the truth of the conclusion is nonetheless still possible and indeed in this case there has been an Aristotle that is/was Greek.

Bringing it back to the current question the ancestor comment claimed something along the lines of (hard to check because it's deleted and in any case I'm paraphrasing):

Terrorists are deterred by airport security checks, TSA provide such security checks ∴ terrorists were deterred

Despite the premise being unclear and thus the logic lacking in rigour nonetheless it is still possible that indeed terrorists were deterred by the TSA.

I don't think you're talking about the same things: a claim of logical fallacy implies that the argument is wrong, but doesn't make any direct claims against the truth of the conclusion. For example, my saying "you should be scared of the TSA, therefore 2+2=4" is fallacious, even though the conclusion is true.

That's not to say that making a claim of fallacy isn't an indirect attack on the conclusion, especially when the only arguments supporting that conclusion are fallacious...

You said: Actually it does [mean he's wrong] because it is upon that logical fallacy that the counter argument is entirely built upon

Wrong is the wrong word :)

What you're looking for is "invalid". An argument is valid if and only if the conclusion follows from the premises. In other words, if the premises are true then it cannot be the case that the conclusion is false. Since a logical fallacy adds nothing to an argument, the conclusion does not follow from the premise. Since the conclusion can therefore be false, even if the logical fallacy is true, the argument is labeled invalid.

Just for completeness... A more strict standard is soundness. An argument is sound if and only if the argument is valid and the premises are true. If an argument is sound, then the conclusion is necessarily true. Obviously, the argument invoking a logical fallacy as its premise is unsound because it is invalid.

It is also perfectly possible for the conclusion to be true even though the argument itself is invalid and unsound.

If you still would like to apply the label "wrong" to it, then I'd say, "The argument is wrong, even though your conclusion happens to be true."

(Note: I can't see the post that started all of this off as it has been deleted, so I'm not making any comment on the truthiness of his/her conclusion)