Belts have been breaking at all sorts of mileages, and often well below 13,000 km. There are various threads on the subject in this forum, with heat being a likely cause but it doesn't appear completely clear.
I've seen something suggesting that the belt needs to be changed at about 14,000 km if it shows signs of wear, and many of them have been looking quite ragged at this sort of mileage, so the dealer may have done the sensible thing (although they should have told you about this before doing it).
Wearing parts aren't normally warranty items but this is obviously a grey area as cam belts on most vehicles don't normally need replacing at 13,000 km either!
I'm surprised they needed to replace other parts unless they made a complete mess of the job, but others may know more about this. They would have needed to move these parts to get the belt on and off but that's not the same as 'replacing' them.
How much did they charge you for the entire job? The belt seems to cost about E140 or thereabouts. Sounds like another nasty bill or a complex little do-it-yourself job... There are some great instructions posted already but it didn't look all that easy and requires some special tools to make the job relatively straightforward. I expect it's one of those jobs that is quiet easy when you've done a few...