The reason that training schools do not offer a decent screening process is as busta says because somebody is about to pay them a hefty sum of money for their training, it is a business and they are not going to turn them away.
In my opinion the screening you are put through can be fairly inaccurate but is still better than nothing. It will often show up the people who just can't do it as well as unfortunately many who can. One person who sat a general GCSE maths test ended up with a big fat zero, is this somebody who would be able to think on their feet in the air by adjusting the headings and times in the hold or calculating rates of descent based on actual conditions? Probably not.
However as is pointed out in previous posts, it depends upon how much you want it, more than the ability you have. Most people can probably do it but there will always be the odd person who just can't.