Just what is Agile Testing?

I seem to notice that I like posing questions in the title of my entries... Anyway, I am currently trying to unravel what exactly Agile testing is. In fact the question could be: how do testers fit into an Agile project? A short Google search tells me that this is still a hot topic, and that there is division over it (an essay from testing.com, Agile Testing, what is it?). I can't help feeling that there is still a silo mentality where each group (development and testing) is going away on their own and deciding what their roles in an Agile project is - which kind of goes against the manifesto.

I have recently witnessed three Agile projects where the testers sat in the same room as the developers but yet both groups built their own set of automated functional tests. This seems crazy to me, but I am willing to accept that I am the odd one out here.

What are people doing elsewhere on projects? Have people been successful in integrating teams as Brian Marick describes, or have you just assumed that the twain shall never meet and focused on getting the developers to produce better code (and functional tests) on their own?

In closing, I do like Brian's categorisation of testing.