On the other hand, like a lot of other good ideas, the agile community has claimed this. A quick google will show that many claim it is a "core agile idea."
It’s absolutely an agile idea. The core of agile development is the ability to iterate quickly. Shift left for certain things enables the cycle to shorten and accelerate iteration.
I agree that it was done by many organizations before “agile” but that’s true of all agile practices. Agile is a philosophy and a collection of tools. None of the tools are new though.