Anyone who claims they can multitask is LYING. The human brain cannot multitask, PERIOD.

You might think you're multitasking, but you are really switching between tasks in your brain. Every time you switch tasks, your brain has to reload the context of what it was last doing on that task. This is not a big deal for small tasks, as the state information is not that much. But the bigger (conceptually) a task is, the longer it takes to reload all the state information into your brain, and the bigger the efficiency hit against you is.
If you find that you can do things no problem by switching tasks, it most likely means that what you're doing is not that mentally demanding, or you are not being effective in what you're doing. A perfect example is if you are surfing the web, watching TV, and twittering at the same time. You might be able to do all 3 of those tasks at once, but no one can argue that any of those things requires more than a sliver of brainpower.