@nevaeh perfectly explained the live search mechanics, but let us talk about the base training data and why Claude might be hallucinating your brand entirely.
Before an AI can search the live web, it is pre trained on massive data dumps like Common Crawl, which is essentially petabytes of scraped internet text. However, AI labs do not treat all data equally. They heavily filter the junk and mathematically upsample high trust domains. Sites like Wikipedia, ArXiv, and GitHub are fed through the training algorithm multiple times so the AI learns to treat them as absolute fact.
This brings us to your question about Wikipedia and brand value. What you are actually asking about is Entity Authority.
If your competitor has a Wikipedia article, a Wikidata entry, or heavy mentions in major news outlets, they become a permanent, recognized entity embedded deep within the model’s neural network. The AI fundamentally understands who they are. If your brand only exists on your own newly launched domain, the AI has no foundational memory of you. When it tries to process a live web search about a brand it does not recognize, its prediction engine gets confused and it starts hallucinating.