In the coworker example, I think the lie was justified given the circumstances, although it doesn't seem to have mattered in the long run and for all anyone knew you could have borrowed a friend's car that day.
Giving your grandmother who may or may not have fallen a comprehensive interrogation, particularly after she may or may not have hit her head seems rude and not very productive. Just for a minute assume she had hit her head, it could have caused her to become confused and fail the interrogation. Another explanation is that she didn't want to stay in hospital and had, in fact, hit her head and was lying to the hospital staff, whereas you interpreted this as lying to you.
It's not clear to me from the story whether or not she fell, it sounds like she fell but you believe she did this on purpose. In any event, whether or not she hit her heard, faking a fall is a cry for help and understanding that might be the more important part of the story.
In this case, if you don't want to visit her, then don't visit her. To claim a moral high ground gained by interrogating her and missing the point of why she would fake a fall seems somewhat off to me.