I would invert that, is Testing "really" a part of how almost all organizations implement Agile. Sure, there is lip service to the issue of Quality Assurance pratices and execution of "some tests" which are often poorly designed by the same person who wrote to the code to exercise the code to "as built" vs "as spec'd."
"Don't worry, if it's broken in production we'll have a new build in three hours...."
I hate the term "Agile (anything)". At the very core, all Agile really is are smaller spoon fed projects with a regular pulse.
Within the Agile realm, you can implemented anyway you like. Some like XP, some like Scrum. If you really want, you can implement Waterfall in an agile way. Just divide the teams into a bunch of different subteams, and have smaller projects and smaller milestones.
Agile is a direct response to the low value that many outsourced QA providers have been supplying to their clients. Where the value added is small, neutral or negative then developers will seek to own the process to remove a layer of low value but high delay outside of their own group. This is what happens when a company sets a price target and not a demonstrable skills target on their outsourced QA providers.
I'm definitely seeing a trend towards on-shoring previously off-shored positions(or at least near-shoring to a similar time zone) due to concerns like that.
But QA definitely has a role in Agile. From helping develop BDD features at the outset and testing throughout the sprint to having dedicated hardening sprints pre-release where full regressions are run.
I use Agile practices every day. the things I generally like about Agile vs Waterfall testing, is the ability to get code delivered in smaller chunks, which can be tested with you and the developer. I am a big fan of having close relationships with the development team, and being able to test right away without having to have a mass of code thrown my way. the other advantage of Agile, is that you can morph it to fit the needs of your team. not every project can benefit from it, but they can benefit from parts of the methodology, after all there are different types of Agile. It is not a 1 way fits all way of looking at solutions.