They can't require that the branding remain visible, unless said branding contains visible copyright notices. Even then, as long as the copyright notices aren't removed, they could be relocated to where you'd put your own copyright notices, and the branding removed.
The whole point of the GPL is to give people the freedom to use and modify the app as they please, as long as others have that same freedom. The requirement that it look the same violates that freedom, and is incompatible with the spirit (and probably the letter) of the license.
Now, they can require that your app not pretend to be the original, and they can require that you clearly identify them as the author of the original code. But they can't mandate that you do it a certain way, other than by changing the name, logos, etc to something else, retaining all copyright comments in the code itself, and displaying an appropriate copyright notice in the usual place in your app.
Disclaimers: IANAL. YMMV.