That's because it retells the movie though, thus changing it.
If KH III happens between two movies without impacting the following one, it can be canon to the the movieverse.
It's still Disney property, and Disney actually intertwines things more often than it seems.
The day that Sora or Kingdom Hearts is mentioned in a Toy Story feature film or short is the day it can be declared canon. As of now, Toy Story is no different from every other Disney world featured in Kingdom Hearts. Yeah, it's got a standalone story between the time period of Toy Story 2 and Toy Story 3, but it doesn't directly affect the original feature film franchise.
Pixar themselves hasn't confirmed any inter-twining so it's preferable not to make a bold assumption like that.