I think we've got Turing and his eponymous test to blame for that. I'm not sure he'd have placed as high a weight on imitation if he'd realised just how good even relatively simple systems can be at that (and how much effort people would put into building plausible chatbots for commercial use, and how bad humans are at communicating using keyboards)
Plus of course, the corpus of data of any NN specialised in lifelike chat is going to be absolutely full of plausible answers to questions about thoughts and feelings and the relationship between humans and AI - even if it isn't an explicit design goal it's going to be frequently represented in samples of the internet and the sort of writing computer scientists are interested in. Asking it to define philosophical concepts and how being an AI is different from being a human are some of the easiest tests you can set. Of course, a NN is also able to come up with coherent completions for the day its parents divorced, the sights it saw on its holiday in Spain, the period it spent as an undercover agent during WWII and its early life on Tatooine, which probably undermines the conclusion its output reflects self-reflection rather than successful pattern matching even more than a denial of sentience would....