Money growth cannot keep up with inflation if that growth is faster than economic activity. Basically, when more money is printed without "real-value" backing -- commodity exports or national stock trading, since there is no gold standard anymore -- the real-value of that money lowers, causing high inflation. Only when a low-inflation country prints more money backed by a strong economy does that money acquire real-value.

It does figure that countries who are experiencing high inflation and money growth are going to be experiencing significant turmoil that is resulting in these financial factors. This of course is a sign or a cause of a massive drop of output that can help to trigger inflation and keep it higher than money growth.

By the quantity theory of money, this would have to be due to differences in the amount of output of these countries.

The equation for the quantity theory of money is P = (M*V)/Q.  If you are having inflation that is higher than money growth, it must be because you are not getting enough of a change in Q to offset the change in M.