How do I convince my father with dementia that he is not constipated?

My parents have been in AL since May and both have dementia in some form but do not require constant care, mostly memory cues and meds. My father complains frequently of constipation. This has been an ongoing obsession, for lack of a better word, for a few years and before moving to AL, he would go to the ER where they would give him an enema. They eventually figured out he was obsessing and would occasionally do an xray to see if there was back up. The AL where they live is wonderful and the staff is doing everything they can to address his concerns without giving him a laxative every time he demands as that will only cause more severe problems. Sometimes they give him a cup of warm water and tell him they mixed his laxative up in it just to satisfy him for the moment. He insists he hasn't gone in four or five days, then a few days later says the same thing. He doesn't have a concept of time passing and I don't think he knows when he's gone or not. I've talked with the staff many times and tried to come up with a plan. One of them even recorded him telling her he'd just had a BM. Then the next day when he again said it'd been five days since he'd gone, she played back the audio and he told her it wasn't him and she had altered it. She even walked in their room right after he'd used the bathroom one morning and could tell because of the smell. That same day, the facility doctor visited him to assess his complaints. He also complains his lower back hurts and insists it's caused by constipation (it's arthritis). They did an x-ray and determined there was no BM backed up in his system. He says he hasn't seen a doctor, hasn't had an x-ray, the staff is lying and he has to be backed up because where is all that food going! By the way, he continues to eat three meals a day plus snacks. If he were constipated like he says he couldn't do that and not potty for 4-5 days. And he takes Miralax and fiber supplements every day (this may change how he goes and the thinks he's not going at all). He doesn't believe that either. He is very angry with me for not believing him and angry at the staff. They understand he doesn't remember and have tried several different strategies to assure him but he refuses to believe anyone. He is still adjusting to not being the one in charge and doesn't like to hear that his memory is not what it was. I don't say "don't you remember?" when he's telling me something for the 40th time but I've had to try to tell him as kindly as possible that he may not remember that he's been to the bathroom. That did not go well! Any suggestions to help him, me and the staff are hugely appreciated.