Zero if you want to understand the situation described in the article, I think you're asking the wrong question, largely of the wrong people.
You're asking a group of people actively spending time discussing parenting and their DCs' university choices, from a fairly informed perspective, why their DCs made a particular choice. Your title prompts self-selection for people whose DCs might have considered Oxbridge - and whose parents know and can talk about this.
Thus you are addressing a pool of people whose DCs could, on the whole, have applied to Oxbridge if they wanted to. The only question is 'did they want to? If not why not?'
What makes you think that volition, amongst the well informed and supported, is one of the more significant barriers to Oxbridge raising their state school entry rate?
Don't you think there might be structural, demographic and cultural issues, some mentioned here but mostly pertaining to people who by definition would not be discussing their DCs university choices on Mumsnet, that prevent many pupils from even thinking of applying?
So the question is, how well have the universities identified those issues and effective ways to tackle them? How are they feeding back to government and schools about this and working together on this issue?