What insurance do people need in assisted living facilities?

My mom and dad are living in an ALF. She is 93 and he is 97. She recently realized she no longer needed to, or could, drive, so she gave me her car. When I called to cancel her car insurance policy, the agent suggested I increase their liability coverage on their renter’s policy. (They had an umbrella policy to provide this coverage till now.) I called the director of the ALF to find out what they require or suggest for residents. She said they leave it up to the residents and don’t even ask what insurance they have. She did say that if someone, say a guest of a resident, were to trip and fall in a common space such as the dining room, the facility would be liable, but that if it were to occur in my parents’ suite, and they were somehow at fault, that they (my parents) could be held liable. The director did say such occurrences are extremely rare, but it is not impossible. She suggested I ask an attorney.
The attorney said it wouldn’t hurt to have the coverage. My dad has mid-stage Alzheimer’s dementia. He is a very sweet, good-natured man, but I realize that later stages of Alzheimer’s could change that. What if he were to become angry and shove another resident, injuring them? And here’s where it gets murkier. I read their policy, and it does not cover intentional acts by the covered persons. What is intentional in a dementia patient?
I will call the insurance agent today to get some clarification, but it seems insurance agents always want to sell you more insurance and then find ways not to pay when you have a claim. There is always that fine print. In this case, it may be that “intentional” exclusion.
What else should I ask, and do they really need this coverage?