Twitter has gotten into the photo sharing game, but not on their own - they've partnered with PhotoBucket.
Apple's WWDC Keynote (which is happening as I write this) tells us why: Twitter is going to be heavily integrated with Apple's iOS 5, the operating system for iPhone, iPad and iPod Touch.
Having worked with for a company that was (and still is) an Apple partner, I can tell you that it probably went down like this:
"Hi, Twitter? Yeah, this is Apple calling. We want to integrate Twitter pretty deeply into iOS 5. You cool with that? Oh yeah, and we're going to announce it next month."
In the interest of secrecy, Apple likely waited as long as they could before contacting Twitter. Once the company understood the time horizon for getting into the photo sharing game, they most likely decided to partner in order to meet the WWDC deadline.
The details of how it really happened will surely surface over the coming months but I'll bet that's how it happened.