Yeah, but decreasing only this infant mortality does not make the individuals live longer. It's just that we have been efficient at removing one cause of death at one end of the spectrum, but not at the other end so much. So as long as you are born and alive, your life expectancy is not really increasing versus people who were alive 50 years ago, after the discovery of penicillin let's say.
This is mainly due to the improvement of hospital facilities and the end of life treatments. we are not living longer better - the older you get the more cripple you are likely to survive. What really matters in life expectancy is the ability to live longer in good health.
The improvement of hospital facilities owe a great deal to humanity's ability to destroy germs at will when it is important to do so, e.g. during/after surgery.
If a baby/child doesn't die, then the only logical conclusion is that it is (and by extension "us" are) living longer...which validates his statement.