What gives the idea that interlinking sites is a bad idea?
The World-Wide-Web is a network of interlinked pages, a website is a group of interlinked pages on a domain. And search engines like Google only index web documents that have been linked to, it is a requirement to ranking and not optional.
Many of the most popular and top-ranked sites are part of a network of interlinked sites, including many examples of sites sharing the same IP address (i.e. Wikipedia is part of a network of interlinked sites on the same IP address).
There is no issue with interlinking sites as long as you do it properly, in a way that is both relevant and useful to users. Interlinking, is not bad, the way some people choose to do it (i.e. webspam) may be bad. Interlinking for the benefit of users is good, interlinking that adds no value to users is bad.