From what I can tell, that assertion is common in Agile advocacy.
But from my experience as a professional software developer in the 1990s, and from reading stories about software development, waterfall was not used at Apple, Be, Commodore, Data General, Infocom, Microsoft, VisiCorp, and more.
That's not to say no one used a (modified) waterfall model. Simply that I haven't found evidence that it's meaningful to say it was the standard development model. [1]
[1] Technically, DOD-STD-2167A's apparent bias towards waterfall was a "standard", but I don't think that's what most people mean in this context, and in any case it was replaced by MIL-STD-498 in 1994, well before the Agile Manifesto.
I don't see much value in debating this. It seems clear to me that the people who wrote the Agile manifesto have experience in working in such, or similar environment and reacted to change it. And clearly that way of working was widespread enough and enough of a pain point to strike a cord. Certainly, when I first read the manifesto it struck a cord and I understood exactly where they were coming from. I think it is spot on.
What raises my hackles is the lack of any qualifiers, given how rarely it's used in the projects I know about.
Of course the shortcomings of this model have been known for a long time to anyone building software and so a number of other models appeared.