Yes. She is renting her router from them. She'll need two things to use her U-Verse connection. One of those things is the modem which takes the U-Verse that's coming in demodulates it into internet access. Then she needs a router which takes that internet access and allows a number of devices to use it. The unit she's renting is probably one box. Sometimes, it's possible to buy that box and eliminate the rental, but it's not possible with U-Verse.
The ability to buy the modem is up to the service provider and/or the FCC. The FCC, for instance, started making cable companies allow customers to buy the modem because they used to only lease it for a monthly fee. So Leo actually bought his cable modem so he doesn't have to pay the rent and has a more up-to-date unit. Unfortunately, AT&T doesn't allow this with U-Verse so Susie will have to continue renting their all-in-one box.