I can think of many reasons, common to many church schools why they get good results - compound effects of things like smaller classes, foundation and endowment budgets that mean they pay better / have more leeway for resources, more seeway in admissions procedures, higher ratio of motivated, supportive parents who have applied form the fringes of the catchement in order to get to the school etc. It's also anly a one-borough study, so the comparison relies v much on the baseline standard of state schools in the borough to be of applied use elsewhere.
In our borough, amongst the 'top' schools, there is a mix of state and church (and secular foundation) - and some seriously under-performing church schools - (not sure what the reasons for that are) - but our borough is also getting much stronger in building the 'added value' scores - improving the results of low achievers - maybe Dagenham hads not cracked this, who knows?
And may be the religious ethos improves education....but I think for this study to be useful in identifying good practice to be picked up elsewhere, (surely the point of any study) we need to know lots more, don't we?