Yes, the symptoms are primarily the immune response. Hence my point that it's probably not smart to interfere with the immune response just because you don't like the symptoms. The immune response is the only thing that will actually get rid of the virus. That sentence from wikipedia doesn't mention anything about an "overreaction".
Well excuse me for not reading your mind as to what you meant by "that." :P
I'm not aware of anything that shows that people who take medications to alleviate symptoms take longer to recover than those who don't, while they're often more comfortable in the meantime. That seems sufficient to establish "overreaction."