Searching on the "open web" in this context simply refers to searching outside the curated experience you might find within a library's holdings, stepping out beyond paywalls and subscription fees that academic libraries maintain to provide trustworthy, credible resources. There are certainly trustworthy sources outside Salmon Library, you'll just need to really leverage those information literacy skills to find the "good stuff", but you need to be doing so at all times anyway! Always be evaluating what you find online (remember the rhetorical triangle evaluation cycle), and pay special heed to the Domains of the websites you encounter. While exploring multiple viewpoints is critical to achieving a more comprehensive understanding of an issue, try and shy away from your .com websites when possible. Try and explore sites ending in .edu for educational institutions, or perhaps .gov for federal and state level publications, or even .org for potential non-profit organizations or research institutes.
One example of a trustworthy, freely available database full of scholarly articles in the below, PloS One. This is a collection of peer-reviewed, highly respected journals in academia on a variety of topics.
Another great open access source is the "Frontiers" series of academic journals, below: