"Entirely independent way" meaning...? Implementing fs-related parts of v7 API is trivial, especially when you essentially don't care about races (and I wouldn't bet a dime on safety of fs syscalls from what-was-it-called... their "stay in background, get woken up on interrupts" kludge... TSR? At most I'd expect them to disable interrupts in what they deemed to be critical areas; most likely would've missed a bunch of races, at that).
So no, I don't think they bothered to nick actual v7 source. But that definitely had been a (trivial) reimplementation of existing interface.
It's about a man-month of work to implement and such reimplementations had been done quite a few times. Including initial debugging, enough to make it mostly usable, if not quite safe. In their case I'd expect the most PITA to have come from making it play nice with the preexisting pile of garbage (FCB syscalls).
If your point was that hierarchical filesystems had turned out to be useful enough for a lot of systems to reimplement them - sure, that's true, but what the hell does that have to do with independent anything? If we are talking about bitty-box parodies on OS, might as well bring Amiga - at least there it really seems that influence might have been not entirely from Unix (I don't know the TRIPOS history well enough to tell, but at least in that case a direct influence from Multics is plausible).
Since late 60s it had been fairly common. And it's simple enough to describe and implement by such description, at least in the basic forms. More to the point, a lot of software depends on having that available, so not implementing a hierarchical fs means serious self-inflicted PITA in porting and redesigning user interfaces. The tricky part is maintaining a sane directory tree layout, but "let's not bother with that" is a lousy answer - all attempts so far seem to have been sucky. FWIW, I'm very sceptical about the tags-based approaches - the problem is real, but I don't think it's solvable that way...
 Once you have to deal with the UCB bad trips (cross-directory renames, handling of dangling symlinks, etc.) the things get more hairy, of course, but that's a separate story.