I kinda both agree and disagree with this. I think you're referring to Arthur C Clarke's third law, "Any sufficiently advanced technology is indistinguishable from magic" - while that is true, I don't think it necessarily follows that all magic is therefore just advanced technology, or even an advanced understanding of the mechanics of the world. To me, magic is something inherently outside the laws of physics - if you're using physics to generate fireballs then to me it's not magic, it's sci-fi.
I do very much agree with you that it'd have been around as long as the species - anatomically modern humans have been around for at least 200,000 years, with the precursors for the several hundred thousand years before that being only very slightly different. I always think that magic should be so inherent in the world that it's something all species posess, since there's really nothing special about humans that should give them magic, but there I digress
On the other hand, I do think it makes sense to work out what influence magic would have had on the development of the human societies - I just think it has to begin earlier. If magic is powerful - such as allowing people to hurl fireballs at each other when they're angry - that would naturally have huge repercussions right from the dawn of time and cause a butterfly effect that would most likely create a completely different society to ours. In my world magic is so subtle and omnipresent that it's used subconsciously by every living being - but can be consciously manipulated to differing degrees (too much detail there to explain briefly though) - which makes it easier to justify a society similar to ours.
That's the problem I have with a lot of generic fantasy - all the different elements (voodoo gods, elves, dwarves, typical humans, etc) are just put in the world together without any thought of how they interacted throughout the hundreds of thousands of years of history to reach the point at which the story begins. Working out how they interact with each other from that starting point to create the future of the world is better than a lot of stuff that I've seen, but it still neglects the majority of interaction between these aspects of the world, which to me usually results in a world that feels flimsy and weak. Obviously then there's the possible solution of making the world a recent creation, but that can be just as complex and difficult as coming up with thousands of years of history - just look at how in-depth Brandon Sanderson's univers appears to be.
That was increasingly off-topic so I think I'll leave it there before I go on any more tangents