I don't see how meditation could cause brain damage, meditation is a mental activity and the brain is a physical organ. Could software damage hardware? maybe if it switched off the cooling fan I guess but otherwise I think its a good analogy.
While mediation should result in not getting entangled or distracted by thought its purpose isn't the end of thought. Thinking subsides in the 2nd jhana but the mind is still active I'd expect, just in a non verbal way.
Meditation, particularly mindfulness, is an active use of the mind. When done right it should be a good way to keep the mind and brain active, even when relatively quiet it takes effort to keep the mind from going all over the place so I don't think you should expect it to result in an inactive atrophied mind or brain.