Doesn't the fact that they scored the same on the first tests actually prove that being rich or poor doesn't matter in practice?

If you give someone a problem to solve and then another one of course he will still be busy with the first. For rich people it's a simpler problem so they solve it quicker.

Of course it's possible to end up in a negative spiral. It's up to society to provide for people on a sufficient level that they can lift themselves up if they are able to.