This is correct, yes. But it doesn't happen because the rich man gets wealthier, it happens because the poor people get wealthier and can afford to buy more TV's, so trickle up rather than trickle down. Because if the TV salesman is selling 100 TV's a year and he gets a tax cut he'll just have more money and that's that, if he's selling 100 TV's a year and his customers get a tax cut there will be more people who can afford a TV so his sales are likely to go up which means he's getting more money and possibly hiring more employees to handle the increased amount of customers. So both situations make Mr TV salesman richer, only one of them is beneficial to the poor people buying his TV's.
Because (at least in a reasonably "free" economy), the same things which result in greater wealth for "the rich" also result in greater improvements to the lives of all those within the same economy (statistically speaking at least). Put in the most direct and simple way: If the guy who owns the TV store is getting richer, it's because he's selling more TVs. Which means that people are buying more TVs. Which means that the people both have more TVs *and* the money to buy them in the first place. Which means that their quality of life (in at least a couple different metrics, and assuming that owning a TV versus not owning one is "good") are better. Not *because* the rich man got richer, but as a side consequence of the same factors that make him richer.
The whole theory of give the rich tax cuts and they'll invest more leans on the belief that creating the room for more supply will increase supply and demand. It's so obviously wrong you could explain it to a 5 year old.
Edited, Apr 12th 2013 3:52pm by Aethien