Well, memtest tests the memory by using it. If as you say the computer crashes when the memory is consistently written to then you should also get a crash or error with memtest. It runs from a CD on boot and outside of Windows so it allows you to insulate somewhat from other factors which can cause crashes.

If you're already convinced that memory compatibility is the problem and it's not worth testing then why are you asking if that's your problem? I'm confused.

Ah ok. Well, if you're going purely off of the QVL then that really won't tell you the whole story. That is a list that they have tested and found good. It is by no means exhaustive and it doesn't mean that anything not on the list is going to definitely fail.

In answer to your question, yes bad or incompatible memory can fail after some time even though it may post initially. That is what programs like memtest are designed to do: troubleshoot a system that posts but has an intermittent issue. Generally though, if memory is incompatible you will find out pretty quickly because it just won't post or if it does you will need to seriously tweak settings to get it stable.

If all you have is a tech telling you that your memory is not on the QVL then I'd say it's a bit premature to go buying new hardware unless your store has a really good return policy. I would start by looking at the Windows event log and see if any events seem to correspond to times that the system has crashed. Sometimes this can point you to a specific part of the system like memory or video.
http://windows.microsoft.com/en-US/windows7/Open-Event-Viewer