Why Do AI Search Engines Sometimes Misrepresent a Source They Cite?

I’ve seen AI search tools cite a page that appears relevant, then summarize it in a way that leaves out an important qualification—or even makes the author’s point sound stronger than it is.

Is this usually a problem with how the system extracts passages, how it combines sources, or how the original page is written? I’m interested in what happens between a cited page and the generated summary, and how readers can tell whether the AI source summary fairly reflects the original argument.