I would hope that it is not controversial to say that multiple on-screen windows are extremely important or even essential for many computer tasks. For web-browsing tasks as well, especially with how many tasks can now be performed via a web browser, there are certainly many cases where seeing multiple browser windows at once is important to the user.
But you asked specifically about "collecting and choosing information on the web." Nielsen included "comparing," and comparing pretty clearly can benefit from side-by-side viewing of multiple windows. If you are only talking about the activities involved in performing searches, reading articles, viewing media, and collecting URLs for reference, then I would also be surprised to discover any benefit to multiple windows being viewed at once. Certainly you can imagine a user wanting peripheral activities to be on-screen simultaneously (such as an IM, music player, or the half-ignored web conference), but the task of "collecting and choosing information" itself doesn't strike me as one that benefits from multiple on-screen windows.
Addendum: Nielsen referenced a decade-old article (http://www.nngroup.com/articles/the-3cs-of-critical-web-use-collect-compareNielsen referenced a decade-choose/old article) which is summarized as "users' most important Web tasks involve collecting and comparing multiple pieces of information, usually so they can make a choice." So he seems to be implying that this most important activity is specifically the kind of activity that benefits from side-by-side comparison of collected information.