I do not believe that web site wide links might positively damage your site, but might they negate the effects of links from that web site? I will be finding out!
Some people question if website wide links could cause damage to your site, but I do not think that any search engine would open the back door for causing harm to another person's web site. But, I do believe that it is budding that they negate the effects of good links on that web site.
Take as for instance, a single link to another site from a well ranking home page. Perhaps that single link does the job and pushes the target page into the top of the search engine results. But, what if the owners of the web sites are working together and decide to get gready and create more links by putting the link into the trailer, or a side bar, of the site? Then there exists the website wide links.
This is what the search engines want to detect and remove and might cause them to ignore that initial good link and in doing so spread the gossip and rumour that site wide links cause damage. It is not so much damage, but preventing the good from being spread.
But, this is a theory and one that is hard to prove or to disprove. However, with a bit of patience and time and a couple of web sites working together then it is budding to test. I have, for this reason, placed a link from a PR3 page to another web site of my own based on a "random" string found on that page.
It needs to be something that other web sites display, that I know the receiving web site is currently being found for, but a little bit of work can push it much higher up the search engines. A tall order! Thankfully, I have a web site that has a 'claim sentence' in it that is used by thousands of web-sites. It is a random sentence and not something that anyone in their right mind would be trying to optimise for.
Except me!
At first, hopefully my site will shoot up from its existing 35th position for the term (out of 30,000 results!). Then, I am expecting one of three reactions once I introduce site wide links:
1 - it will stay at the improved position, showing that they cause no harm
2 - it will tumble below position 35, showing that site wide links are positively damaging
3 - it will return to round the 35th position, showing that, as I expect, web site wide links only cause the links between the websites to be ignored.
What good is knowing what these links do? Well, as a designer of numerous websites I may discover that I am being damaged by the copyright statement on the hundreds of web-sites that I have built because they have site wide links. Understanding more about their impacts will allow me to decide whether to remove links from trailers or whether they are safe to be left there.