AGI is just a type of AI. It's a term coined long after AI that doesn't define new goals and capabilities that weren't already part of AI research, except that they were rather abandoned. If anything, "AGI" was the marketing term to revitalize and focus on those ideals. So there is nothing wrong with the general public to associate "AI" with what you would specifically describe as "AGI".
Furthermore, I don't understand what this public perception has to do with your claim. If they thought of only narrow AI, then would it not make even more sense to call their LLM-based products AI...