No, it wouldn't be a week because you could buy them over the summer and have to wait until the next ski season to see if they were defective.
Seriously dude, you need to rethink what a warranty is all about. They are only for manufacturing defects detected within a year. It does not mean that they have to replace any product within a year. They didn't break because off Dalbello's mistake, they broke because you used them for 6 months. When you ski on something for 6 months, it gets worn, it gets old, and it breaks. You're saying that the liner broke when it wasn't supposed to, well, heavy use is what makes things break, that's when it is supposed to break.
Now, that being said, lots of ski companies are very flexible with their warranties and will replace just about anything without even asking. I guess Dalbello isn't one of those companies, but it doesn't seem like they are being unfair to you.
I like Dalbello though, so I'd like to see you get a new liner. Just raise a big fuss and see if they change their tune. I'm telling you though, you may have to call them and talk to someone and lie about how much you used them or under what circumstances they broke.
If they never replace that liner you have a few options:
Sew it up yourself in about 10 minutes for $2
Buy a new liner, you can even talk to Dalbello over the phone and see if they'll sell you 1 liner
Or upgrade to ID liners for like $100