Is it possible for someone with dementia to seemingly get better?

Medications can often help those suffering with certain types of dementia; is there any history of mental illness at all here, as well. Are you the POA for health care? If so are you aware of what the medications are?
Many medications for hallucinations and paranoia require a blood level before they begin to work well. Same for depression. Stopping these medications suddenly can have some dire results. And while the blood level of the drugs will work for a while without taking the drug, eventually the effect will wear off and it is likely back to square one.
And do understand that all dementias are a bit like a simon-says game in the beginning, going one or two steps forward and then one back. They have good days and bad days, especially in the beginning. Anxiety can often provoke bad episodes.
I am assuming this person was not visited by a sudden change that could have been stroke related? Because often stroke symptoms can leave within the first two weeks; strokes would be of sudden onset.
Good luck on your medical mystery tour. Update us if you find out anything.

We just went through this with my dad who has dementia. He has good times and bad times but just spent 5 days in the hospital for paranoia and saying that people were outside his window telling him they were going to kill him. The hospital determined he had become dehydrated and that caused his bizarre behavior. So after 5 days in the hospital on IVs, he said he felt great and wanted to go home. The doctors said 'no' because they said the dehydration will happen again and that dementia patients often lose their sense of thirst. Possibly this may have been part of your relative's 'recovery'. He ultimately had to be moved to assisted living and is now drinking and eating much more with the help of a 24 hour beverage bar they have there. Doctors said he can no longer live on his own at home.

I doubt seriously if he has “gotten better”. I think you’re right when you say he’s hiding it. He’s angry he was hospitalized and with his mental issues, he’s probably very paranoid that if he acts out again, he’ll have to go back to the hospital.

Just my opinion, but he probably should not be living alone. Is he being supervised by any agency or a social worker? If he is angry with you and accusing you of stealing from him, I would definitely limit my contact with him.