Given that both the story and the character designs are quite different from the game, and the fact that later animations of TYPE-MOON works stayed much closer to their respective originals, I would assume that TYPE-MOON did not closely oversee the anime adaptation of Tsukihime, or influenced its production greatly.
But I don't agree that the anime sucks. It's very different from the game, so you could defend that it's a bad adaptation. But as a TV series it did quite well, at least according to the numbers on English-language websites: (82% with 3300 votes on ANN, 74% with 26000 votes on myanimelist). Its license was announced six months after airing, which was quite a normal timeframe in those days.
Also note that the anime is called Shingetsutan Tsukihime, not Tsukihime. So even though there technically is "no Tsukihime anime", and it would be extremely nice to get a more faithful adaptation, the animation stands perfectly fine on its own.