Who invented the crossbow? From the state of Chu right?

The Wu-Yue Chunqiu 《吴越春秋》, a history of the Wu-Yue War of the Spring and Autumn Period written in the Eastern Han, credits the invention to a Mr Qin 琴 from Chu. However, the book contains material that is of doubtful credibility and may just reflect legends current in the Han.

since native groups throughout asia have used crossbows, I think it's one of those things that just came around, like spears, bows, and leather armor

The equipping of the crossbow as a regular shooting weapon was not begun untill the Spring & Autumn period according to Yang Hong again, probably originating in the southern state of Chu. Yun's comment is probably based on the same source as the books conclusion.
Chu was noted for fine weapons though, and it was one mechanism on the ATARN site that was commented on as finer made than Qin.
Hong also records the conversation recorded in the histories of Wu & Yue where the King of Yue asks General Chen Yin about archery and was essentially told that the crossbow came from the bow, which came form the pellet. Chu-qin placed the bow accross the stock and installed a trigger mechanism. Thus the crossbow was born.
Whether it is factual or not as Yun suggests is impossible to say, but there probably won't be a better or easier answer than that.

From the state of Shu, prior to the state Nan-Yue and Zhao Tuo, the magic crossbow was invented by the An Yang Wang, it was called Lien Chau (Lien=continuous Chau=treasure), just one shot for 10 arrows all at once.

However, King Anyang (An Duong Vuong) from Shu is said in the legend to have lived at the time of Zhao Tuo, towards the end of the Qin. He invaded and conquered the Au Lac around 210 BC. So this is not earlier than the story from the state of Chu.

King AnYang was a historical person, not legendary. Story about the magic crossbow was a legend but the crossbows as weapon were historical.