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I understand that scientists should be cautious about too readily accepting new findings. But sometimes they make sweeping statement themselves based on their own narrow findings.

In fact, there is some very good evidence showing that brain training does improve cognition:
Susanne Jaeggi and Martin Buschkuehl's study on Improving Fluid Intelligence by Training Working Memory (PNAS April 2008) recorded increases in mental agility (fluid intelligence) and short term memory of more than 40% after 19 days of focused brain training.

I was so impressed that I contacted the research team and developed a software program using the same method so that anyone can achieve these improvements at home.