You're not really taking on board what I am writing.
We are both in agreement that pinyin is a romanised form of the Chinese writing system.
Each letter combination corresponds to a Chinese phoneme, although this is not an exact science
Many phonemes in mandarin have no English counterpart. In that case approximate letters are used
So far so good.
Now, in English, the letters x and z are used interchangeably at the start of words. So someone who wants to write Xi may write Zi, for no other reason than thats what they are used to. It may not represent the sound in pinyin, but as far as I can see, the original tweet was written in English and if you think Rudy Guilani is aware that the pinyin sound for x and z are different, then so be it.