Though an accurate mainstream statement, it is not quite true. The idea that inertia is an intrinsic property of mass is really a hold over from a Newton, even perhaps pre-Newton concept of matter. But is does retain a hold on the mainstream view. Where it is not quite true, even from a mainstream perspective is that, within the context of the Standard Model, the mass and thus inertia of fundamental particles, emerges from their interaction with the Higgs Field. That would make at least some part of an object's inertia, emergent rather than intrinsic.
This transition, from fundamentally intrinsic to fundamentally emergent, moves a step further in the context of some of the work and ideas of Puthoff, Haisch & Reuda, who suggest from within an SED context that inertia emerges from an interaction of the fundamental charged particles matter is composed of with the zero-point field, as the object moves through the field. In which case inertia as a whole would be emergent rather than an intrinsic property.
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Now to my vote. I vote yes, but I qualify that as being made from a classical everyday experience of inertia, where we can certainly measure the inertial force of a moving object as it impacts a scale and the force of gravity with every step up a staircase. So my yes, is based on that everyday experience.
I don't believe we can say with any certainty what the origins of inertia are, at this time. The answer it would seem to me lies at a quantum level, and very well may involve an interaction with the ZPF.., though from inertia to gravity seems a hard stretch right now, following that trajectory. Still, though classically I say yes, I am more inclined to favor a fundamental origin of inertia, as an emergent quantum scale interaction, rather than an intrinsic property.
It really seems to me to depend upon from where you look at the question.
