A good and careful doctor is not going to diagnose dementia simply based on the results of the MMSE. "Oh, 21? Here's your dementia diagnosis. See ya!"
When my father was diagnosed, the doctor did include much of the MMSE. But he also interacted with my Dad for a good 45 minutes. He did a complete health history and physical examination and medication review. He listened to my input and concerns. In my Dad's case the internist happened to be a new doctor to my Dad because his previous internist had retired, but in an ideal world, a potential dementia patient would meet with their doctor for years and so the doctor would form a baseline impression. IIRC in our conversation the doctor was paying attention to reported changes from baseline too - "Dad used to be able to manage his medications but has had mistakes lately" and "Dad always paid his bills on time but now there's a messy pile" and "Dad's making more reminder notes for himself and is forgetting things he normally would remember."
I'll also add that at least in my Dad's case, we were wondering about dementia for a while before his diagnosis. Then it become abundantly clear over the past two years or so. Mostly it's just been supportive type care and no specific treatments, and since we would have done that stuff anyway, the diagnosis mostly just helps us understand what's going on and maybe deal with it in a better way.
It's worth mentioning to anyone still reading that it's important to rule out other stuff that can result in dementia-like symptoms but are treatable conditions. I think the biggest one in the elderly is UTIs, but there are others. Obviously one would want to identify and treat anything treatable before resigning themselves to dementia.