Hej Devalanteriel, as a native English English speaker I would stay it's more precise to say stood but more people I suspect would say 'put' if they were focussing on the action or 'is' if they were focussing on its location, and 'is stood' if they were focussing on the action but indicating the orientation of the object.
In this way, it seems to me that this matches the Swedish, where the use of more precise verbs of position and orientation are used (ligga, stå & siiter) in preference to just using 'is' or 'vara'. In English tis is equally as possible but less frequent. Equally with lägga, ställa & sätta we probably are more likely to say the generic 'put' but many people would be more precise as say is laid, is stood and is sat. All to say, that we have the same distinctions as Swedish and they are and sound perfectly okay, it's just that they not as frequently used.
If you have small children; I'd think the floor is the last place you would set a drinking glass... OK, though, I do understand how one would place a window glass on the floor or lean it against the wall but this sentence is still just very odd to me; like they should have used a different object or a different place to put the glass.