The other way round is much much worse - imagine if rich people don't invest but rather just consume. It _takes_ away money from poor instead of building more wealth for everyone.
So the overall point being made here is not that true
Now an even better outcome would be that rich people didn't get rich in the first place. This would mean lower inequality, which in the data correlates with higher growth. This is demonstrated convincingly in Piketty's work.
Overall, if youw ant to maximize growth for the poor (or really, growth for all of society at an equal pace, say), then you would want to dramatically raise taxes on rich people and eliminate the class entirely (IE, no more rich people). That would massively stimulate growth and of course skyrocket the wealth of currently poor people.
It's a bit sad that the solution is so simple and has no downsides.