Morozov is wrong; you just don't know the history.

Keith Bostic has gone on record as saying that he was inspired by Richard Stallman to try to make a fully free version of BSD. The GNU tools were a crucial tool on every Unix by the mid-1980s, and indeed played a major role in making Unix useful. While you can argue about whether it was a good idea to try to rebrand Stallman's "free software" movement as "open source", it doesn't make sense to argue that Unix was somehow unconnected to the free software movement.

Furthermore, there was already a movement afoot to build software under free-software licenses in commercial companies many years before the Open Source Initiative was founded: Sun, DEC, HP, and so on, were members of the X Consortium, which continued the development of X-Windows as free software many years after its original (academic) maintainers had stopped; Cygnus effectively took over maintenance of GCC and the rest of the GNU toolchain from the GNU project by about 1990; Sun published NFS, Yellow Pages, Sun RPC, and so on under free-software licenses starting in the mid-1980s, and later funded development on Emacs; Lucid forked Emacs to form the basis of its IDE, giving us XEmacs and its high-quality open-source C compiler, lcc. None of this was "regular academic sharing of ideas" — while these were companies with academic roots, they were judged by standards of business, not academia — and it all happened on Unix.

And many of the people who built that open-source software that made Unix what it was were also founding members of the Open Source Initiative.

At the same time, there was perhaps an order of magnitude more programmers using IBM PCs under MS-DOS. The only significant open-source software I can think of from this era on that platform is the various open-source FORTH systems. There was lots of user-group and BBS-scene software, but it was usually distributed without source, or occasionally with source, but under "no commercial use" licenses — you could maybe even put the IBM PC BIOS source code into this category. There were occasional exceptions — the WaZOO source code from Opus, say, or PC-HACK, ported from Unix — but not many.

So I think that it's perfectly fair to describe the "code sharing involved in Unix" as a unique nascent movement, separate from the "regular academic sharing of ideas", which at some point decided to (mostly) call itself the "open source" movement.

It's not entirely spin. The free software movement was largely a reactionary movement to various attempts of that era to take the "academic sharing of ideas" back in to the proprietary fold. It (and the later open source movement) was very much trying to defend/establish/whatever the environment under which Unix evolved.

So it is not so much retroactively claiming it as open source as it is acknowledge open source's heritage.