Yuki does not have the ability to create data, nor does the data thought entity. Haruhi does though.
The Data thought entities manipulate the data around them to do things like moving back in time, or changing an object. For example, when Kyon requests Yuki to create a large rain shower on the day of that baseball game, Yuki tells Kyon that causing a rain storm would cause a large environmental disaster in the eco system. This is because to create the rain, Yuki has to turn something into the water, which would cause an imbalance. Secondly, Yuki has not reconstructed reality, there's a large differece from what you call reality and what's going around in the novel.
Yuki has caused events in the past to not occur preventing
Spoiler! :
Also, Yuki obtained the power to manipulate data from the Data Thought Entity. I'm guessing that with a certain amount of brain power, you should be able to manipulate "data". Also, I believe that circumstances must also be met to manipulate data.
It'd be a blatant lie if I said that I understand 100% of what I just spewed out