The Players Handbook does not support any specific world over another. The sample characters, domain descriptions, and other sections in the book use examples that cover the gamut of game worlds. The list of deities in Appx B in the PHB covers 4 ancient earth pantheons (Celtic, Norse, Greek, and Egyptian), and the major game worlds for D&D (Forgotten Realms, Greyhawk, Dragonlance, and Eberron) as well as the 'non-human' deities.
The 'multiverse' has been publicly stated to be the default setting as a whole, thus being inclusive of all game worlds simultaneously and allowing cross-overs between game worlds.
Does the #dnd tabletop RPG have one official setting? The answer is yes. That setting is the multiverse, which includes all #dnd worlds.
Although the quote given from escapist magazine by Mike Mearls all but says the FR is the default setting, the date on that is still in the pre-release phase of D&D (2 June 2014), and Jeremy Crawford's statement was in January after the DMG was released, thus the more current comment seems more reliable in this case.
However, the adventures coming out for at least the initial two campaigns and encounters seem to be exclusively focused on Forgotten Realms. One of the first two campaigns is based on a story that has a very Greyhawk feel, and is based on an old storyline from Greyhawk (Elemental Evil, out in March/April). The first campaign is based primarily on Forgotten Realms, but the story would take very little conversion to move to Dragonlance in particular, substituting Thakesis for Tiamat. The flavor is very similar to a Dragonlance story.
Yes, the current material focuses on Forgotten Realms right now, but this is primarily as it relates to the Adventure League and published adventures. The overall statements, to me, seem to imply that they wanted a generic and inclusive world that they could put an infinite number of stories/campaigns and would be well received by the fans overall, and Forgotten Realms has historically made them more money than any other established game world due to the popularity of the setting and the novels.
In short the Core Rules don't favor any game world, but the other released materials point toward Forgotten Realms. The developers' statements seem to focus on the multiverse as a whole, but individual printed campaigns back up a Forgotten Realms bias.