Crazypilot and 367outbound as far as I am aware, the only course at Oxford that currently requires potential students to undergo an aptitude, ability and attitude assessment procedure prior to starting the course is their 'APP First Officer' programme. Indeed, a post on 9th of this month on their forum by their Marketing Manager, Marty White, reveals that the only way to attend this selection procedure is to apply for the APP course and pay the required £195 to do so. Naturally, some people will fail this selection.
However, students who opt for the standard Oxford integrated course, or elect to purchase Oxford's modular products (other than their forthcoming 'Waypoint' product, and then only at a late stage in the course), face no such selection - and thus cannot fail it. This is no different to the majority of schools; many schools offer flying training products to whoever has the money to pay, and there is no reason why they shouldn't do so. The risk is purely financial, and is fully accepted by the customer in the contract with the FTO.
CTC, for better or worse, has chosen (as far as I can see) to put pretty much all its eggs in one basket: becoming a training provider to the airlines, rather than to the potential pilot (although the training is largely at the potential pilot's expense - but that's another argument!). Thus all its students face a selection procedure, and one which is essentially uninfluenced by the student's ability to pay. Oxford's APP is superficially similar, though their approach is in fact still contracted to the student rather than to an airline, and is intended to make the student as attractive as possible to whatever airlines are in the market at the time of the student's graduation. Thus the student's ability to pay is paramount, as there is no airline effectively underwriting the student's loan at the commencement of training (though I do accept that OAT 'facilitate' the loan).
I repeat: this is in no way a criticism of Oxford. It is simply a statement of the consequences of the differing commercial approaches taken by Oxford and CTC.
Scroggs