Exercise can delay the onset of dementia. I wasn't aware it has been claimed to slow its progress.
There are observational studies that associated exercises with delayed onset of dementia, but they cannot show the direction of causality - it could be that people who are healthier and not at risk for dementia tend to exercise more as a result.
There are RCTs showing improvement in cognitive function in healthy older adults, which one might hope means that the onset of dementia is delayed - but that has not actually been shown.
If you're well educated, alert (maybe from exercise?) and so on then the early signs of dementia may just be less obvious. If you forget a few names but can do the cryptic crossword or run a mile then relatives will not push you to get tested.
The assumption is exercise results in higher blood flow which does "something". I know its easier to concentrate when you have practice concentrating, and for many boring people, exercise might be their only daily experience with concentrating, aside from the rare occasional dementia testing. Possibly forcing concentration on a regular basis (via exercise, or whatever alternative) results in better cognitive test results.
I suppose a lot depends on defining exercise as staring at a TV while walking on a treadmill vs playing racquetball.