The problem is caused by some iOS releases. Two devices running the same iOS can handle the calendar file in different ways depending on the upgrade history.
The results of my tests on my devices are:
iOS 4.2.1 prompted to open in Dropbox or Evernote. The iPod Touch 2nd generation was upgraded multiple times.
iOS 5.1.1 displayed a call for action and then handled the file correctly. iPad 1 was upgraded twice.
iOS 6.1.5 and 7.0.4 worked perfectly well. iPhone 4s was upgraded twice, iPhone 5 and iPad Air just once.
iPod 4th generation and iPhone 4s, running 6.1.5
iPad Air, running 7.0.4
iPhone 5, running 7.0.4