Husband got agitated when the nurse was trying to assess him for memory care. Now they say they can't take him. What do we do now?

There has to be more than 1 Memory Care Facility in your area.
And what did he do ? what did the nurse do to agitate him and what did the nurse do to calm and reassure him?
I would imagine if you went there for a visit, tour and you were sitting in an office and the nurse was trying to ask him questions he was tired, confused and just ready to leave. The longer the questioning went on the more anxious he would have become. I completely understand his side of this. (when my Husband wanted to leave someplace there was nothing that would get him to change his mind!)
I suggest you either ask for another appointment or schedule an appointment at another facility. Go at the time of day that is best for him. If he is on medication to calm him make sure you give it to him before you leave the house. And if there is a place he likes to go schedule that after. (my Husband would have been fine if I told him we were going to get something to eat after).
Also if this evaluation was being done in a closed office ask if it can be done someplace more open so he is not confined.

What actually happened during the assessment?

"Got agitated" is a bit vague. Could range from declined to interact with the nurse so that she couldn't do the assessment, to started banging his head against a wall, to tried to throttle her. What was your opinion of how the nurse behaved towards him? - was she unsuccessful in calming him, or did she not even try?

What feedback did the facility give you? If they couldn't do the assessment, they can't admit him as a resident. Were they proposing another appointment or refusing him outright?

Well, I think that you dodged a bullet with that one.

ANY memory care facility that will not accept a person that gets agitated is not really a memory care facility.

You are going to have to find a facility that actually works with Alzheimer's and dementia, not just a warehouse type place that only wants compliant, well behaved residents.

Have you checked into board and care homes? Some are very good with difficult people and they have a better patient to staff ratio.

I know that you feel overwhelmed because of this, but step back, take a deep breath and start looking for a facility that can deal with any behaviors. You know more now, use that knowledge to ask your questions and make your decision based on what you know today.