If that file were to be removed, presumably the archive would again be served up upon request.
The lawyers were asking for the archive store itself to be wiped.
The Internet Archive has a mechanism for doing this, as I understand it. It involves asserting copyright over the material in question and essentially "making a case" for removal. IA decided the case they made didn't pass muster, and denied specific removal on those grounds, which is why they mention "journalistic nature of the archive" and so forth.
But that's entirely orthogonal to their policy of treating active maintenance of robots.txt as indicative of positive copyright assertion over the contents of an entire domain -- which Ms. Reid's team appears to have taken as a fallback position. They couldn't get the sanitized archive they wanted, so they just made the whole thing invisible.
They say they "declined to take down the archives"-- but they didn't in fact do this at all, they just insisted a request to take down the archives come in the form of a robots.txt, and they automatically and without review comply with all such requests in the form of a robots.txt. They don't in fact ever decline to take down any archives, if the request is properly given as a robots.txt.
I don't know why they bothered making statements about "declining to take down the archives" in the first place (to the journalist or to us), making comments about "Reid’s being a journalist (a very high-profile one, at that) and the journalistic nature of the blog archive" -- they did not in fact "decline to take down the archives" at all. The "journalistic nature of the archive" was in fact irrelevant. They took em down. They are down.