Earlier quoted context omitted.
You had me until, "it's a really good signal when they pull out their phone and add it to a to-do list." Because it's just one of many possible courses of action for staying organized. For all you know the guy added it to his to-do list on his way to the car, or maybe he employs some other mechanic. While you could argue that an interview is a showboating environment where one is expected to signal certain desireable…
It's a signal. It's not a binary yes/no, there are many observations we're making throughout the interview. This is just one, and the to-do list isn't the only correct answer. Asking me to email those details to them is another possible right answer. Writing a note in a notebook is fine. The key thing to remember here is that we're asking this very much in the middle of the interview, and I just want to see that they…
Unless your request was very specific and strange ("send me the completed k3-45 and t9807 forms"), in which case I'd have to jot /that/ down.
Should you not rather evaluate whether your request was fulfilled?