J.T.
My husband is an insane researcher on everything we purchase - and I have a very acute sense of smell so this was actually a big deal for us when we purchased a wool rug. Apparently, there are different kinds of glue/backing that can be used on a rug. What we couldn't find is any info on if his smell is dangerous. In my opinion, if it smells bad/toxic, it just can't be good for you.
My sister in law has a PB rug in her house and it's the first thing I smell when I enter - and the smell has never faded. However, the smell isn't just from PB rugs, we found lots that smell during our shopping(all that use this certain glue). We did purchase one from PB that they SWORE didn't use this glue but, upon delivery, the smell was very strong (and the glue was listed on the care label). After a few days you could smell it throughout our entire 2 story condo and it gave me headaches so we returned it.
I'm not sure if any of this helps - go to PB and smell a few rugs they have hanging up. You'll notice it immediately and, if your daughters rug does not smell that way, perhaps it is a different fiber and backing and is safe. Good luck!