The problem seems to be in the way Xbox Music for Windows Phone has been designed. The app cannot switch to another connection once it starts the streaming process. And when you lock the Windows Phone screen, it turns off Wi-Fi connectivity.
So basically, when you lock your phone you’d have Xbox Music eating up the pricey data from your carrier plan and not Wi-Fi.
Of course, that is probably not a huge deal for many people, but for those who have to pay overages, or care about preserving their data longer, this could be a big annoyance.