Heinlein stated writing "Friday" in 1981. This is well after Vannevar Bush's highly influential "As We May Think" from 1945. It's hard to find someone in information retrieval in the 1950 and 1960s who wasn't directly influenced by Bush's Memex. One of those is Ted Nelson, who coined 'hypertext' and wrote "Computer Lib / Dream Machines" in 1974. This book in turn influenced the early microcomputer hackers, which is the era when Heinlein wrote Friday. (Eg, Jerry Pournelle started writing for BYTE in 1980; there isn't a huge gulf between SF and microcomputers.)
You regard Heinlein's 'dead-on intuition that such systems will naturally lend themselves to browsing by associate leap' as being prescient. I can't say what you mean by prescience, but I can point to "As We May Think" to show the importance Bush placed in associative thinking some 35 years earlier:
> The human mind does not work that way. It operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts, in accordance with some intricate web of trails carried by the cells of the brain. .... Yet the speed of action, the intricacy of trails, the detail of mental pictures, is awe-inspiring beyond all else in nature.
> Man cannot hope fully to duplicate this mental process artificially, but he certainly ought to be able to learn from it. In minor ways he may even improve, for his records have relative permanency. The first idea, however, to be drawn from the analogy concerns selection. Selection by association, rather than indexing, may yet be mechanized. One cannot hope thus to equal the speed and flexibility with which the mind follows an associative trail, but it should be possible to beat the mind decisively in regard to the permanence and clarity of the items resurrected from storage. ...
> Wholly new forms of encyclopedias will appear, ready made with a mesh of associative trails running through them, ready to be dropped into the memex and there amplified.
I can also say that in 1951 Heinlein was well aware that research was much more than 'narrow document retrieval'. Consider "The Puppet Masters" from that year, chapter IV:
> "At the library I went to the catalogue, put on blinkers and started scanning for references. "Flying Saucers" led to "Flying Disks," then to "Project Saucer," then "Lights in the Sky,", "Fireballs," "Cosmic Diffusion Theory of Life Origin," and two dozen blind alleys and screwball branches of literature. I needed a Geiger counter to tell me what was pay dirt, ... Nevertheless, in an hour I had a handful of selector cards. I handed them to the vestal virgin at the desk and waited while she fed them into the hopper."
That's catalogue-assisted associative thinking, followed by document retrieval. I don't think requires prescience in the early 1980s to get a sense for how a Memex-like machine embodied in a modern computer might improve upon a paper catalogue for associative thinking.
To be more concrete, remember too that France was rolling out Minitel across the country the same year Friday was published. While Minitel specifically did not likely influence Heinlein, I bring it up to show that the ideas of online research terminals was no longer pie-in-the-sky dreaming, but something that many people thought about and were implementing. (Another example from two years later is the 'the Bloomberg terminal', which is now a mainstay of business research.)