The model says that Chess improvement requires large amounts of information be committed to long term memory. If that model is correct, then Chess improvement, especially for people with no previous Chess history, would be slower among older players.
That doesn't mean that anyone is too old to improve. It just means that older players would have to work harder for the same level of improvement.
And of course, the model hasn't been confirmed. It was good enough for one guy to get a PhD, but that's hardly the same thing as being the consensus of the scientific community.
Top level old men are very uncommon. How many old men made it to be world champion? I can only think of Steinitz and Alekhine.