I don’t remember if it’s true that the brain can’t make new cells (as I recall, in depends on the type of brain cell – ‘brain cell’ is kind of catch-all term, and there are many different types), but what is more likely happening here is that exercise is improving blood flow to the brain, which is what the neurons feed on (remember your little cell respiration chart from high school bio?), so they’re performing like carbed-up marathoners. This increase of blood flow probably also helped the brain to produce new connections between neurons, which is where memory really “lives.”

I won’t argue, exercise is a great thing. There’s a great deal of research showing that exercise improves memory in humans, too. But it’s about blood flow and the number of neuronal connections, not the number of brain cells.