I think maybe
I'm considering applying for Philosophy at Cambridge because that is truly my passion, I absolutely adore it an enjoy nothing more than reading Philosophy. However, this doesn't stretch to all my University applications, that is, in most places I'm applying to read Law for pragmatic reasons.
It would surprise me if anybody could get a place at Oxbridge without a passion for their subject. It's very intense so you'd have to be committed to survive really. However equally I think it's more likely that people who get places at Oxbridge tend to be more passionate because they can afford to do pleasurable subjects due to the great employment prospects.