Regardless of the rules interpretations...
Another fun thing for players who spam detect magic is to place magic where they don't expect it. For example, Sovereign Glue (a magic item) could be used to repair something relatively mundane, like a statue. Potions can spill and end up being tracked around on peopes shoes, leaving "magic" footprints. When a magic weapon is broken it is still a magic item, and pieces of a sundered bow or quarterstaff can look awfully strange so someone who doesn't know what it was originally. Any of these things, and countless others, can drive players crazy if they get too caught up in using Detect Magic.