Clonal and subclonal mutations in cancer
They don't really contradict each other; the clonality of neoantigens adds an extra layer over the overall mutational load ; but overall mutational load (and consequently overall neoantigen burden, because mutations in a fixed sequence context generate neoantigens at a certain rate) by themselves are also predictive. 

Tumours with a high neoantigen burden tend to generally respond better anyway (See Snyder et al, NEJM , Rizvi et al, Science and Van Allen et al, Science) and also the fact that mismatch repair deficient cancers generally tend to respond. 

So if you take high neoantigen tumours already (both lung and melanomas have extremely high mutation burdens), and then stratify them based on neoantigen clonality , you tend to further stratify patients by response associating with checkpoint blockade. 

The whole point of McGranahan et al was to point out that it is possible to raise immune responses that target all the cells in a tumour, and that the ability to do this may dictate survival in general and checkpoint blockade response in particular, but only when antigen presentation and immune infiltration are intact. McGranahan et al note that clonal neoantigens do nothing in Lung squamous cancers because of depleted CD8 infiltration and MHC class I expression and there is other work (See http://www.pnas.org/content/113/48/E7759.abstract )  

As for this bit


  Plus, probabilistically how likely it is for a certain cancer lesions
  to have lots of shared mutations? A totally genetically homogeneous
  lesion with no branches with a very high number of mutations.


That is quite complicated to answer; but as a general rule it is worth remembering that,  as the number of divisions and the number of mutations (and ergo prospective subclones) increases, for tumours to stay clonal it requires extremely strong selective sweeps so that at any given time a very small number of clones tends to predominate, and at least in untreated/pre-treatment tumours, there is the tendency for a lot of them to show effectively neutral patterns of evolution ( http://www.nature.com/ng/journal/v48/n3/abs/ng.3489.html )