Would alzheimer's patient speak two different stories to different people?

Hi

We have place my dad in a nursing house and we have hearing different stories from family members that he is not happy and needs to leave the facility. When it come to us (my brother and i), we have met him several times and he had not shared any major concerns. After 3 days staying at the nursing house, he has asked us that he wants to leave and once we did some activities with him, he changed his mind And stayed.

It is a difficult decision to take and thus always feel worried if it is the right time to place him in nursing home.