Why do links and mentions make search engines and AI trust a business?
Because they are evidence from someone other than the business. A company calling itself the best proves little. A local newspaper, an industry list and a trade body naming it in their own words proves more. Search engines have counted links as endorsements since Google's early PageRank work, and links are still one input among many. AI assistants read the web as text, so a mention with no link at all still teaches them who the business is.
Consistency adds to the effect. When several independent sources describe the business the same way (same name, same services, same city), search engines and AI have something safe to repeat. Quality beats volume: one feature on a respected local news site tells engines more than a pile of weak profiles.