Yes, while it is true what you stated, that "When there is a rumor about something, most people are going to go digging to find out the truth and form their own opinion," the problem is all the information (and disinformation) those same people will have to wade through before they get to the truth. It also raises the following questions for me:

1- what information is already available online about my company

2- is it true or not

3- how many results appear before my information is located, etc.

People rarely go past the first page of results in Google searches - think about your searches. How far do you go - page 1, page 2, further? We often do the same when shopping on Amazon. If your own information that you know is true is buried, people will rarely see it, if at all. This is why SEO (Search Engine Optimization) is critical, so that your information moves to the top.

It is also a good idea to review what is online at least once each month, just to be sure and ready. This is what a good marketing and/or public relations team will handle.