Rich people may not eat more food, but they may eat food that is shipped in from all over the world. They don't drive dozens of cars at once, but they do have lots of things delivered, and tend not to take public transport as much. They also tend to fly a lot more (which is a big source of emissions), and live in big houses with lots of lights and area to heat and cool.
I agree with your point that a carbon tax would not serve the purpose of a UBI. Now I'm gonna go off topic a bit and focus on carbon taxes.
I volunteer with Citizens Climate Lobby. The bill we're trying to get through the House of Representatives, H.R. 763 aka the Energy Innovation Act, is a carbon tax, but it's not like you imagine, I think. It taxes fossil fuels at the point of production, and therefore allows normal market mechanisms to adjust the prices of everything. No change to individual tax bills. Some things would get more expensive, but we would all get a check in the mail to offset. If you pollute more than average, the check wouldn't make up for the increased prices, but if you pollute less, you'd benefit. The change in prices will shift consumption away from the emissions-intensive goods and services, toward those that are greener.
The poor would disproportionately benefit from this. Not just financially -- carbon emissions and pollution that affects health are of course closely linked, and it's poor people who suffer the most from pollution, because they can't afford to move somewhere else to escape it.
It's not just about individual behavior -- companies would feel the same shift in incentives. Another way to think of the tax, from an economist's point of view, is that it's just correctly pricing a market externality.
The weird thing about a carbon tax like this is that a majority of Americans support it, but most of us don't think that it's a majority! It's already popular, we just have to convince Congress.