Actually, that's not always true.

The first year you are abroad, you may have to file form 2350 (application for extension of time to file US income tax return) BEFORE April 15, because you may not meet the criteria for a tax home in Switzerland by the automatic extension time of June 15th (you must be in Switzerland for 330 days during any period of 12 consecutive months). This is true for those of us who move late in the year5. If you must extend until after June 15th, you must ask for a special extension before April 15th (since you wouldn't qualify for the automatic extension on June 15th).

By the way, when you send in form 2350, don't expect any feedback from the IRS, but you can call them and they'll tell you if they've received the form. They're actually surprisingly nice about these things.