The doctor is absolutely correct. The T in TIA stands for Transient. It's not transient if post stroke symptoms continue. Most of us don't have one TIA, however, we have several (or many,) but the analogy to waves is right on--there can be cumulative damage. There are such things as small strokes, though, that leave long-term damage, even if you Moms remember them only as a bad headache, or some tingling in an arm.
The general term "dementia" is a term for a cluster of symptoms, not really a diagnosis. (Sort of like high blood pressure--a symptom of many diseases.) But vascular dementia is a very real, very scary, diagnosis just like any other cause of dementia symptoms, including Alzheimer's. What ever vascular problem--spikes in blood pressure, small bleeds, narrowing of the blood vessels, etc--is causing the dementia will continue to bring more decline until it is addressed, and, even then, the damage may be done.
Having had a small stroke recently, I can tell you it got my attention and I will be modifying eating and exercise habits!