I'm not convinced the "evidence" is suggesting anything without further data, and this article is glossing over "correlation != causation". Without a baseline (a situation where, over the same years, tuition fees weren't introduced/raised), how do we know what the equivalent situation would be? Perhaps there would have been even more people from poorer backgrounds applying.
It is evidence. No need to put it in scare quotes. We can debate the correct interpretation and applicability, but it's certainly evidence of a sort.
It's impossible to run the kinds of controlled large scale socio-economic experiments you describe. If we ignore the evidence that doesn't meet your high standards, we'll have no real world data.
Recently it was discovered that working 20 hours a week while going to school results in worse grades - after decades of believing the exact opposite. When they did better studies - comparing like students (same school, same background, and other characteristics), they discovered that all the prior studies were just showing the success of students who really should have been even more successful. So I prefer to think of most studies such as this as a datapoint, rather than any type of evidence.
You might want to look up the definition of evidence. My reading of three definitions just doesn't quite match your definition. But no big deal. I think we agree, and this has become about word interpretation.
* No comparison with other time periods, and their respective tuition fees.
* No comparison with other countries, and their respective policies.
* No data on where these students graduate from, or in which subjects, or with which grades, or what their average salary is X years later, or whether they'll actually be able to pay back the loan.
It's missing a huge amount of important information; you really can't justify the conclusion "tuition fees are good" from this alone.