In Agile Teams - A Plumber is a Plumber, and a Painter is a Painter
One of the things that Agile discipline encourage, and preach is that everybody should be equal on the Agile team, and although there are different activities, some people on the team will be experts in doing one thing, and others experts on another thing.
Well, I guess I would not want my plumber to paint me a painting, nor do I want my painter to fix my pluming... I would not want the plumber to fix the roof of my house, or the roof builder to touch my pluming... etc'. a Plumber - even though knows how to fix a roof - will never be as good as someone who is a professional, with long years of experience, and methodological and theoretical knowledge in that area.
A developer - under this assumption - can test, but will not test as good as a professional tester on an Agile team. The same happens when a tester will develop software on the same Agile team. Yes, he can develop code, but no, not as good as a professional developer.
It is the same also on classical development models: testers are doing automation, but automation is writing code, testing it in low level as well (unit test). We - testers - are good and professional in testing. In Quality Control. Not in developing complex code.
So, the focus in Agile teams should be about communicating and bringing the best knowledge of each one of the team members on the Agile team to be visible to the other members. His/her knowledge can help the team go through the challenges that the company is facing, while others in the team can learn more about it.