But it isn't just a case of memory. His claim is that he could view individual droplets, whereas if time was passing normally it would just look like a normal stream from a shower.
What is more likely:
1) Time actually stopped behaving as it normally does in some guys bathroom at the same time as he suffered from a brain aneurysm that caused a 'large patch of neural damage'.
2) The guy's perception of time was screwed up as a result of the aneurysm
3) They guy's memory of his shower is partly or entirely confabulated as a result of the aneurysm
Considering the article you linked to speaks about how interruptions to the perception of time are relatively common, names some regions of the brain that can influence time perception and repeatable experiments that show this happening. Consider Temporal Lobe Strokes and Epilepsy.
I have a clear memory of coming off my bike when the pedal snapped off. I had considerable time to think as I rolled over backwards and the bike went over top me. I remember clearly thinking that I was wearing a white jacket that was going to get dirty and then I casually thought that I'd better put me chin on my chest so that I wouldn't crack my head on the pavement. I have no doubt that in some sense time slowed down for me.
Your brain realized it was an emergency and maximised processing - meaning you could think more thoughts, make more discriminations, make more decisions to try and maximise your dealing with the emergency leading to the illusion that time slowed down. It has a name:Tachypsychia.