I think this is a very important concept that shows us a few things about design.
For one it confirms that people aren't going to read or look at everything so we must be very selective in the amount of data we present which is often hard when you have a client that wants way more information then will fit. Perhaps we should link those clients that article.... probably not though lol
It also shows us where on a page the eye is likely to go first so that we can better decide what the primary data is vs the secondary data vs the somewhat arbitrary design elements. Why put arbitrary design elements? Because every aspect should be designed and whether it is a rule on a page or white-space it should be considered. If you read more on that website or order the book (I just ordered it but haven't gotten it yet) you'll see how alignment and obstacles occur in designs. We should be creating compositions that present the data in a visually clear manner and design elements can be used to guide, divide and join elements together.
I'm in the school of thinking that the end-user's experience is the most important. Perhaps this is wrong but I think we must consider our end-users before our advertisers.
Should we ALWAYS follow this guideline though?
I think the answer there is no. But perhaps that no is my print background speaking and when there is very little content on a page so that it is easy to see all of it.
It seems that in reasoning this out from my experiences as a designer the more content you have the more important it is to use a more standardized layout. A poster with one word on it can put that word anywhere while a page in a book or magazine should certainly follow standardized formats to avoid confusion.