We all have the problem now over moth and no Fix from Apple also not on iOS 6.1.
Many user are loking for the reason of this problem.( No sound from Video Music or other App`s over the speaker, but ring tones are ok. )
I think it must be easy to c or any other should have the possibility to make an downgrade form the iOs to 5.?????.
If than the problem still exist it should be an hardware problem.
If not and this is my opinion the problem is Apple responsibility. Than Apple has with iOS 6.0 made this problem, and destroyed my iPhone 4. This all in the 24 warranty moth in Germany if Apple is also the dealer of the product. As in my case.
I Have Apple Support contacted but the problem is up to now not fixed.