Various analysts and other sources have been indicating that the iPhone 5S could launch as soon as June or July, but MacFan's specific claim of a June 20 media event seems to defy common sense on several levels.
First, while Apple has not yet announced dates for its annual Worldwide Developers Conference (WWDC) in San Francisco, a tentative long-range schedule that leaked several years ago and continued gap in the Moscone Center's public schedule have suggested that the company is likely to hold the conference the week of June 10-14.
Apple could certainly choose to introduce the iPhone 5S at WWDC as it did for several years before it shifted iPhone launches to later in the year for 2011 and 2012, although the company has shown that it is willing to hold WWDC without a major hardware launch and instead focus on iOS and OS X for its developer community.
Still, even if Apple chooses not to introduce the iPhone 5S at WWDC, it seems extremely unlikely that the company would expect the media to return for a separate media event just a week later to show off the iPhone 5S. Even when it is running a tight schedule to launch significant numbers of new products, Apple schedules significant gaps between its announcements in order to allow each one to have its full share of publicity.
Second, Apple almost universally holds its media events on Tuesdays or Wednesdays, with the theory being that Mondays are poor days for members of the media who may need to travel to the event location the day before and that Thursdays and Fridays don't leave enough time for the full publicity impact before the news cycle is interrupted by the weekend. The one recent exception to Apple's scheduling trend was its education-focused media event on Thursday, January 19, 2012, but that event was unusual in several respects, including its location in New York City and a strict focus on content such as iBooks Textbooks and iTunes U rather than any new hardware.
As a result, we believe that June 20 is a very unlikely date for an iPhone media event, with Apple being much more likely to either introduce the iPhone 5S at WWDC itself during a Monday keynote (regardless of what week the conference is held) or at a Tuesday or Wednesday media event at least several weeks removed from WWDC.