DZ, and the memory of all the people who lived there (at the time) was created by the Fayth 1000 years ago. Since Shuyin lived in Zanarkand at the time as well, the Fayth would have no doubt created a dream version of Shuyin as well, 1000 years ago at that time. But the problem is, we see Tidus in present day Spira. It's impossible for Tidus to be the memory of Shuyin that was created 1000 years ago that still lives in the present, because Tidus is 17 years old, not 1017 years old. The idea of a time freeze is also out of the question, since we see flashbacks of Tidus when he was a kid talking with Jecht, and thus time flows normally in DZ.

There's also the fact that the Fayth do indeed clearly remember who Shuyin is. Bahamut's Fayth talks about him in FFX-2. But probably the biggest problem with the "Tidus = Memory of Shuyin" theory is that the fact that their names are different. If the Fayth was trying to create the memory of Shuyin, but knew his name was Shuyin, why is Tidus not named Shuyin?

How the Fayth create memories doesn't matter at all. The simple fact is, we know that DZ and the people that live in DZ (i.e. Shuyin) were created 1000 years before FFX started, and we know that the Fayth do remember Shuyin's name. Tidus was born 17 years before FFX started, and is not named Shuyin even though the Fayth remember Shuyin's name, so he isn't Shuyin.