You are discussing two separate issues.
One issue is the concept of trading links.
The other is avoiding the use of the word "link" or "links" wherever possible. It is also about a directory file having anything that says "links.htm" in the coding.
Trading links is fine provided the other person is willing to make a fair exchange and doesn't use any "dirty tricks". Unfortunately, they do happen. I have a discuss on "Linking: Avoiding dirty tricks
" on my blog.
Should you exchange links, that is a more complicated topic. When you do trade links with other sites, do so with your visitors and customers in mind. In other words, stick to the themes and topics of your site. Not only will your visitors appreciate it, but so will the search engines as they reward theme related links, and discount those that are off topic.
Avoiding the term "links" in every possible way is good for the search engines as well. They are tending to ignore "links.htm" pages entirely. That means little or no passed along Google PageRank or link popularity boost. It's also better for your visitors if they see your links as Resources or something similar. Think in terms of helping your visitors, and they and the search engines will help you in return.
Hope that helps a bit.