Wouldn't their nursing home percentage be lower because of the out of control nature of the virus in the rest of their population compared to the rest of the country?  Seems you are giving them credit for having a worse infection rate and response in the rest of their population that made the nursing home percentage lower in comparison.
		
		
	 
I think that the data suggest NY's nursing home situation isn't a murder field related to other states that were also hard-hit by the virus. Fact is this population bears the brunt - and not just because they are old, but due to their inability to quarantine from staff that circulate the facilities and are exposed to the outside and inside infected foks, I'm sure.
I spent some time this morning going through census data for demographics and nursing care facility populations. Note that I don't know what is fully included in the "nursing care facility" per census - obviously nursing homes, but I assume also long-term care facilities? 
I calculated your risk of dying (so far) in a nursing home as nursing home deaths / nursing care facility population.
I also calculated your risk of dying (so far) as a 75+ year old person in that state (assuming this is a reasonable estimate for over half of nursing home populations and also the most at risk of dying in a nursing home outbreak). 
I called the ratio your relative risk in a nursing home in that state (how many times more likely to die). Note that this isn't 100% accurate as it wasn't just 75+ year old people dying in nursing homes. I also looked at 65+ to evaluate this. It is also below.
I understand the basic issue of "if you don't have a lot of deaths in your state and you have some nursing home outbreaks, then it is going to skew your nursing home death percentage." And, you actually see that with Delaware, IMO - a state with only about 200 total deaths but over half of them from nursing homes. Rhode Island is similar. But when you get into thousands of deaths like these other states - I think it becomes meaningful.
Here is a table of the results for risk relative to non-nursing home 75+ population and then for non-nursing home 65+ population. 
 
