What does "standard" mean to you?
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.