Not sure if the absent-mindedness is really a symptom of anything other than the availability of other means of storage.
There's an old Egyptian legend about the god of wisdom (Thoth) offering the written word to a pharaoh and being rejected on the grounds that writing things down will remove the motivation to remember.
Now we have so many other places where we can store our memories (especially visual and auditory memories) it wouldn't be surprising if we had difficulty remembering things stored digitally. I'm ashamed to admit, for example, that I don't know my wife's mobile number because something else is remembering it for me.
One interesting experiment based on the storage of almost every experience and possession
is described here.
I myself have a USB hard drive and if it ever got lost it'd be like a case of amnesia to me...or maybe Alzheimers. Not sure really.