Xi spend two months in Iowa. You can't pick up a language that fast. Also that was years ago, when he was already an adult.
He also did not have any English education when he went to school. When he was in Iowa he was there on government assignment, which means there would be a translator with the group.
Even for kids, picking up a new language is hard in two months.
Also remember Chinese and English as vastly different. If a French speaker pick it up in two months then its believable.
You think Xi didn't prepare for his summer trip to the US? That's rather unlikely, isn't it? Also, the phrase "working knowledge" is key. For example, I have working knowledge of Chinese, but it only means I could understand basic social communication and not much further. For business and technical discussions with my Chinese colleagues, I use a mix of Chinese and English- Chinglish. When I travel in China and watch local TV news, I don't understand a lot of the words, but with basic-level of Mandarin, I could sort of follow what's going on. Of course, the TV pictures helps a lot, but even with out it, working knowledge of Mandarin allows me to follow the story... kind of.