I imagine there's all kinds of variables at work here. Is it a "simple idea" short story? (by which I mean, is it really mostly about getting to sharp idea or twist?) - if so, then concision should be king and everything else should be blown away with Chekov's gun, because it's all about achieving the effect, tightening momentum to reach goal. If it's more of a character piece, than I guess more implied detail is not only okay but kind of expected, as it rounds the piece out a bit (the art of small details implying larger ones). If it's both, then loose detail is okay, but less so than a pure character piece.
Probably part of the problem is that we're talking about genre work, implicitly, but not being more specific than that. I mean, I assume that heroic fantasy short fiction and world-building SF short fiction readers adore those kind of "floating drapery ends" of details because they do the same thing they'd do in a non-genre piece, imply a larger world, but in a much more evocative way because the world isn't real. But me, I don't really have much time for world-building, I like attempted realism with a small twist, mostly. The hardest to write.
The two things I think might be relevant here are:
If the implied, untold "larger story" this feels "part of" is more immediately, obviously compelling than the story you just read, this registers as a cheat or anti-climactic to the reader, especially if they LIKED the story up until the moment they realized that the other one (that they have NO assurance they will ever get - this may seem old-fashioned in the internet age of instant access, but you still don't know)) is actually better. It's like waking up and gradually realizing you're on some funky little schooner, admiring the woodwork and the cooking smells, and just as you step onto the deck to view the sunrise, an enormous cruise ship with naked people laughing and drinking on deck, bejeweled sails a'flappin' in the wind, passes you....heading a few degrees away from your course. Look, there it goes...
I guess the other point may be the individual tolerance for series stories. Generally, I don't like them too much. Oh, they work well in certain genres (fantasy, sf) than others (horror) but, even when they do work, I HATE the feeling while reading that scattered details ("oh no, that call from Margwar the soulless on my answering machine again!") are all planted there to be spun out into their (*giggle*) delicious little own stories...whether they deserve to or not, whether you desire it or not (call it bur- out from reading too many comic books in my youth - Chris Claremont is never going to tell us why Dragonfly was on Muir Island that one time, is he?).
I'm not saying it (serialized stories) can't be done, or even done well, but it always makes me feel like a lab rat when all I signed on for was reading a story (again, though, this really has to do a lot more with temperament and genre type, and also whether you know going in that it's a series story). I personally think telling a self-contained, resonant story is a hell of a lot harder than telling a story packed with teasers that the writers may want to "expand on some day" - but, again, I realize that in some genres that's almost an expectation nowadays - everythings a potential serial, radio show, breakfast cereal, lip balm.
Do the work, punch the clock, round the ends - write me a whole story, I say. YMMV.