I dunno, even if the site was updated by a non-Jew, there's still a halachic problem. There's a principle called Ma'aseh Ma'arat Ayin, literally, "Deeds appearing to the eye". It's a Rabbinic prohibition against doing anything which appears sinful.
The idea is that if a person known to be an observant Jew did something that appears to be sinful, someone could see and think that either A) The deed is not a sin or B) This person is sinning. For example, if a Hasidic Rabbi was seen drinking a glass of milk with a hamburger, even though it was coconut milk, one would think that it's okay to drink milk with meat. In this case, since the text body of the web site mirrors Chaim's speeches, and the date of Shavuot appears right below the JTF logo, one would assume that Chaim updated the website himself. Whether or not these assumptions are skin deep, the fact that they can be drawn is problematic.
From where I'm standing, it looks like the prohibition of Ma'aseh Ma'arat Ayin was violated.