Max,
It has been said that the most dangerous lie is the one that begins with a shred of truth.
What you said about there being only one controller in the tower, and him giving taxi instructions and takeoff clearance, and then turning away to do administrative duties, is a fair representation of what "they said." I take great offense, however, to your editorializing "their" remarks by adding your own "totally forgeting [sic] to watch the flight."
Point 1: The "they" that you're paraphrasing said nothing about the controller forgetting to do anything. You are putting words in their mouth. That's unfair.
Point 2: By inserting the word forget, you imply that the controller did something wrong. You imply he sould have been watching the entire taxi and takeoff, and he was negligent. Now, while we may find out later that observing the entire taxi and takeoff was part of his assigned duties, and he failed to do them properly, such has NOT been stated or implied by the person you paraphrase. So far, we have only heard suggestions to the contrary. He was NOT required to observe the entire taxi and takeoff, and he was not being negligent by turning around to accomplish administrative tasks.
Would it have been nice for him to watch and possibly catch the error before it resulted in death? Well, certainly. However, that alone (being a nice thing) doesn't make it the controller's error if he did not. Don't place negligence where negligence has yet to be established.
.