I haven't read the article or what ever that started this thread only the commnetary, but what I have read suggests that what Ms Birbalsingh suggested was that by obsessing constantly about Oxbridge, children were not being given enough encouragement to look at all the other universities they could go to.
Oxford and Cambridge are not the best universities for everybody, nor are they necessarily the highest rated place for every subject. DS's Faculty at a non-Oxbridge University is rated the best in the country and Oxbridge is not even in the second position, and that applies to a number of subjects.
Students should choose which university they want to go to on the basis of the syllabus it teaches, not its place in the University hierarchy. DS's school would really have liked him to have appied to Oxbridge but because Oxford did not offer the subject he wanted to study as an undergraduate course and the Cambridge one was not to his liking, he refused to apply to either and applied to those universities that offered the syllabus that most met his study ambitions.
Most employers know which universities offer the best degrees in the subject they most need and I suspect, for example that most engineering companies rate a degree in engineering from Imperial College well above a similar degree from Oxbridge.
IF that is what Ms Birbalsingh is saying, then I am in agreement with her.