Agreed. One of the things I think is wrong with lying in general is that it can mess up the incentives for behaviours you want to see more of (i.e. a white lie to your friend, claiming to like her awful haircut, doesn't do anything to help your friend improve her future haircuts.) In my example, I'm lying with respect to my first-order desires, but telling the truth according to my second-order desires. I may first-order want a few more minutes to drink tea and socialize with the other nurses, but I don't endorse myself wanting that, and I certainly don't want to encourage my patients to not call me because they're worried I'm too busy or tired or cranky. I second-order want to encourage the behaviour where my patients call me for all the little things and 90% of the time it's annoying and stupid but 10% of the time it's super important.

If I ever had a patient with a rationalist background, maybe I could explain all of that, but maybe not even then; most people aren't at their best for following complex logic when they're loopy on drugs or having trouble breathing or whatnot. So I go for the emotional reassurance, because that gets through. Still working on different phrasings, and I don't always succeed; I was helping out another nurse with her patient who had diarrhea, putting her on the bedpan every half hour, and at one point she fell asleep and pooped in the bed while asleep and then cried with frustration the whole time I changed her, and I wasn't able to reassure her.

Well, that's a good idea right there. You could tell them: "Please don't be embarrassed, and don't hesitate to call me. You're in an ICU and it's very important that you communicate with us, even if it's just a matter of discomfort. You shouldn't assume you can tell the difference between something trivial and something serious, or something that requires immediate attention and not."

You can expand "Don't worry about it" to include permission to bother her. "Don't worry about it - please never give it a second thought if you need me for anything. That's what I'm here to do."