I know plenty of guys and gals who ride track with 3/32 chains w/o issue. I know the BMX kids who worked at our shop would sometimes jump on recommending 1/8 chain, but I don't think it is really an issue.

Again, this is not a "normal wear and tear - use the opportunity to upgrade" issue. This should not have happened (unless you did some sort of sillyness the bike was not designed for/got in a crash/etc. However, when you do stuff like that, there are usually signs of wear other than just a bad bottom bracket. If you were riding silly (read: tricks) or had an accident, then this is a "bad luck sucks, pay for it" issue). Ask them to replace it. Don't be a jerk, but explain that you think this problem falls well outside normal issues, and that they should warranty replace it. Politely ask for the owner/manager if necessary. Again, be nice, because if they do work with you, you can use this as an positive opportunity to build a good relationship. If they are unhelpful and keep trying to push you to upgrade, then you can say something snarky like, "I certainly won't upgrade at a place that doesn't stand behind their products," burn the bridge, and find a new shop. Seriously, I would go for a manager/owner right away, because they are more likely to want you to have a positive experience, and the shop guy you worked with might not have the authority to OK replacement issues like this.