It is entirely possible that she is writing a track for Eurovision, just not necessarily for the UK.
But if both these rumours prove true then good grief...
EDIT:
Also, to echo the poster above's point I am not sure that Sam Bailey is even signed to BMG any more (if she ever was), goodness, I am not even sure she is still with a label that's part of the same parent company to BMG, as far as I know she is with a label called 'Tiger Drum', a label that as far as I am aware has only been in charge of releasing her second album and nothing else.
So unless BMG as signed/resigned her for this, this would mean that BMG, as part of their debut year working with the BBC to provide an act and song for the UK in Eurovision gave them a song by someone that wasn't with them until recently and a song by someone who works for another label.
Still, we'll see, this may be just me trying to find excuses and reasons why something so potentially terrible won't happen to reassure myself that I won't spend the weeks leading up to and after Eurovision telling people the reason we were going to lose/lost is not because of politics but because we send bad acts.