That's correct. There's nothing wrong with throwing away styrofoam if it's disposed of properly (i.e., buried in a landfill).
The Wikipedia paragraph you link to cites three issues:
1. "Styrofoam takes a very long time to decompose in the environment." True, and as I pointed out before, this is a GOOD thing if you're trying to keep greenhouse gases out of the atmosphere. But, more to the point, "in the environment" means that it's littering the ground or floating in a lake, river, or ocean. The whole point of a landfill is to take things like styrofoam OUT of the environment and bury them safely.
2. Styrofoam "has been documented to cause starvation in birds and other marine wildlife." Yes, if they eat it. Which means we're still talking about styrofoam in the environment, not in landfills. If it's properly disposed of in a landfill, birds and marine wildlife will not encounter it and cannot be harmed by it.
3. "In the categories of energy consumption, greenhouse gas effect, and total environmental effect, [styrofoam?s] environmental impacts were second highest, behind aluminum." This has nothing to do with landfills -- it's talking about the production of styrofoam, not the disposal of it.
So I stand by my statement that styrofoam buried in a landfill is not harmful.
Now, we can talk about the environmental impact of producing styrofoam if you like. but it's important that you examine the environmental impact of whatever you are proposing to replace it with. In the case of the Epcot gardens, you suggested that the styrofoam be replaced with clay pots. In environmental terms, are those better or worse than styrofoam? The firing of pottery involves heating it to temperatures of 1000 degrees or more in a kiln. If the kiln isn't electric, that means burning fuel of some sort and releasing the waste gases and ash into the environment. If it is electric, then we have to examine the generating plant that produced the electricity.
I don't have any idea how much pollution is produced by making clay pots. It may pollute less than manufacturing styrofoam; it may pollute more. Without specific numbers to compare, we can't make a rational choice.