Yes, so press for an honest opinion, making clear you are willing to hear the truth.
Too often schools find parents ask but don't want to hear the truth,so make vague noises which could be taken to mean lots of things, to avoid upset. If you are direct and explain you don't want to waste your and his time on things which are unrealistic, then I think they will be more precise.
- you could ask what his KS1 SATs indicate
- what he is on track for with KS2
- what percentile the school would place him in - not just in the school cohort, but nationally
For the schools you mention, the school need to be telling you that DS is extremely able, one of the brightest they have seen in recent years, is in the top 10% as an absolute minimum, is exceeding age related expectations by a considerable amount. Simply being told he is on the top table or gets 80% in tests isn't precise enough or an indicator that he is more than a commonly bright boy. And that's what you want to know isn't it - is he fairly bright, is he very bright, is he exceptional.
Of course there will be schools for all of the above. However the schools you name want the exceptional or at least the very bright. And they will only award scholarships and bursaries to those who are the best. That's a very small number of kids. It will be great if your DS is in that category. And if he isn't, there will be other schools to suit him....but the reality is that bursaries and scholarships tend to be given to those at the top of the pile.
Best of luck working through it all.