Or maybe she's a member of a college sports team which made its own hoodies for the Doxbridge tournament?
having been on the doxbridge tour twice now i can say that no colleges, oxford, cambridge or durham use the doxbridge logo on doxbridge stash, they make their own college hoodies and put doxbridge on the back.
In fact, i have a hoodie of a similar design that you're talking about, if i wandered regularly around palace green i'd think that you were maybe refering to me...