That's it exactly. If he had pleaded not guilty to manslaughter, much more evidence would be being shown. As it is, the fact that he killed he, he was in her flat etc is not contested so there's no need to prove it
The fact that she was attacked, killed, put into the back of a car and VT was seen shopping shortly thereafter works in favour of VT having accidentally killed someone but it also suggests a calculatingly creative alibi (one he hopes will work). He even texted his girlfriend from the store to say nothing.