This is an argument of semantics more than anything. Like asking if Linux has a GUI. Are they talking about the kernel or a distro? Are some people going to be really pedantic about it? Definitely.

An LLM is a fixed blob of binary data that can take inputs, do some statistical transformations, then produce an output. ChatGPT is an entire service or ecosystem built around LLMs. Can it search the web? Well, sure, they've built a solution around the model to allow it to do that. However if I were to run an LLM locally on my own PC, it doesn't necessarily have the tooling programmed around it to allow for something like that.

Now, can we expect every person to be fully up to date on the product offerings at ChatGPT? Of course not. It's not unreasonable for someone to make a statement that an LLM doesn't get it's data from the Internet in realtime, because in general, they are a fixed data blob. The real crux of the matter is people understanding of what LLMs are, and whether their answers can be trusted. We continue to see examples daily of people doing really stupid stuff because they accepted an answer from chatgpt or a similar service as fact. Maybe it does have a tiny disclaimer warning against that. But then the actual marketing of these things always makes them seem far more capable than they really are, and the LLM itself can often speak in a confident manner, which can fool a lot of people if they don't have a deep understanding of the technology and how it works.