I've read the CDC guidelines and you are at best not being fair in your interpretation of the guidance. Here's CMS guidance based on CDC's recommendations.
https://www.cms.gov/files/document/3-13-2020-nursing-home-guidance-covid-19.pdf
And if someone sick with CV19 isn't admitted back to the home, or must be kicked out when diagnosed, the next question is where do these people live, especially in hard hit areas where the nursing home deaths were highest? Maybe in retrospect the feds or states seize a couple of unused hotels and staff them up with skilled nursing home care, and send them to those hotels, but otherwise, there aren't obvious options. Many residents don't have alternatives other than that facility, and those facilities are privately owned, so how do you force some kind of arrangement where one business gets the sick patients, and another keeps those not infected, etc.
So this thing about blaming CDC for nursing home deaths is fine but it's 20/20 hindsight and I'm sure most of the problem is facilities failed to achieve the guidelines because protecting any population that lives closely together is just damn near impossible of the virus is widely spreading in the community. So in Tennessee we had outbreaks in nursing homes mostly in Nashville and Memphis, because that's where we had the biggest outbreaks. In Knoxville, ONE nursing home had more than 1 case, and it had 4 cases, they diagnosed them, contained it, and had one death. My mother in law's place had ONE case, they effectively isolated her, and that was the only case so far. So nursing homes can protect the residents when the case counts are low. It's much harder if you find out 1/4th are sick, THEN try to isolate the remaining residents.
Point is the reason for social distancing is to reduce cases in the community, and where there were low cases in the community, there were FEW bad nursing home outbreaks. When it's running loose in the community, yes, nursing homes got hit hard. But that's because social distancing failed, basically.