Basically, the way you want to think about it is, no, they can not give sources. That information is not in their neural net. It can't be. There isn't anywhere to encode or represent it.
What they can do is make a guess what a source might look like, but even if they are right, it is only because they happened to guess correctly, not because they knew the source. They don't. They can't.
It isn't that "they give sources but they might be wrong", it is "they will make up plausible-sounding sources if you ask just as they'll make up plausible-sounding anything else you ask for, and there's a small chance they'll be right by luck". For more normal factual-type questions part of the reason they are useful is that there's a good chance they'll be right by what is still essentially luck, but for sources in particular there's a particularly small chance, by the nature of the thing.
Maybe human intelligence is more like that than we're willing to admit ;)
Here's an exercise you can try: Cite some information from the next issue of Science to be published. Cite anything you like from it.
You can make some plausible stuff up. You could make even more plausible stuff up if you went and scanned over the past few issues first. But without specific knowledge of the contents of the next issue, you aren't going to be able to create real citations. This is what LLMs lack, by their nature. It's not a criticism, it's a description.
You can't guess sources. The possibility space is too large, the distribution too pathological, and the criteria for being correct too precise.
GPT will never cite sources correctly. Some future AI that uses GPT as a component, but isn't entirely made out of a language model, will be able to, by pulling it out of the non-GPT component. Maybe it'll need to be built as an explicit feature, maybe it won't, only time can tell. But expecting language models to cite sources correctly is not sensible. It's just not a thing they can do.
https://news.ycombinator.com/item?id=33841672
That example is a few months old but OpenAI doesn't seem to have made much progress there, it's still trivial to reproduce