You read horror stories on forums for one simple reason, people come here when they have problems.
Not many people join and post becasue they love their car and its running smoothly, most join becasue they need help. The forum would be packed if EVERY fiat driver was here instead of just the ones with problems lol.
As for reliabilty, this is my second one. My mk1 was bought with 60k on the clock, ran it for 10k, sold it and made a profit and the only repair was a pair of rear shock absorbers which was my own fault (long story involving a bump in a road lol)
My mk2 so far......the slave cylinder went not long ago, bout 40k on the clock. wasn't a fault, was down to the road again. Hit a bump too hard and was changing gear, the rod moved and as I released the clutch the rod split the cylinder (very messy lol)
So basically they are good reliable cars as long as you maintain them properly. And if anything does go wrong they are fairly simple machines and can be fixed for a lot less than other cars.
Take a look around next time your out and count the punto's you see, there are hundreds of them. And there is a reason for that