Everything that you say in your question is correct, and to address your reliability concerns, as part of certification the FAA requires certain hardware testing (EMI testing, decompression testing, etc.) of any EFB, including the iPad. They are not however, certified to the same standards as avionics, because a failure of an iPad does not create the same safety issue as other certified parts.
Beyond the testing for certification, there is required testing by the certificate holder before any update may be applied at the end user level, and part of the approval process requires written contingency procedures that are approved by the FAA for use in the event of a failure of the iPad(s).
Typically, at least two are required in the cockpit for dispatch unless the paper equivalents of all electronic documents that they are approved for are available (charts, operations manuals, AFM's, flight logs, etc.). If they failed prior to takeoff, this is likely why they returned to the gate. There are contingency procedures for an in-flight failure of a single iPad, and for failure of all iPads on board. These are written by each applicant but typically require "anticipated information" to be manually recorded from the working iPad, or using another source (FMS, ATC, data link, internet, satellite phone, etc.) to get the information if they both fail.
The FAA has a ton of guidance/requirements available for those wanting to use COTS hardware for EFB's. Also keep in mind, that using an iPad as an EFB is only a few years old, but EFB's have been used much longer than that. Typically in the past, a Windows based tablet computer was used (talk about reliability issues), and the procedures so far have worked quite well. I don't know of a single accident caused by an EFB failure.
Whether or not the iPad is on the MEL depends on the class of EFB that it is certified as. If it is certified as "carry on" equipment, then it is not required (other than by company policy) so will not be on the MEL. If it is "installed/mounted" in the aircraft, then it may be listed in the MEL.
For lots more information, see:
AC 120-76C - Guidelines for the Certification, Airworthiness, and Operational Use of Electronic Flight Bags
how has a piece of consumer electronics got into the safety chain, well, you said that youknow that these devices have been certified for use. that's how. – Federico Apr 29 '15 at 12:34how they got into the loopis and remainsthey passed the certification process– Federico Apr 29 '15 at 13:17Are they MEL items? Does anyone know what's really going on here?– Simon Apr 29 '15 at 14:07the app proved “extremely stable” during testing. In the “unlikely” event of a software crash, he says, it takes but a moment to get them running again.Clearly not. It's a consumer device, on second thoughts, why am I shocked? – Simon Apr 29 '15 at 15:53