No idea where you saw that info, but the tag works without the phone being nearby. That being said, just like Apple's, the Smart Tag uses Samsung's network (i.e. Samsung phones around) to get and send location data... If you're in the US, needless to say, the userbase of iDevices around is much larger than Samsung's. So, in less populated areas, an Apple Tag is more likely to be able to get and send data from phones around it than a Samsung one. But if you're in a larger metro area or fairly-populated areas, you should be fine (I live in San Diego and so far haven't had an issue getting a location ping for my dog and my keys using Samsung Smart Tags).
If you want better coverage, I'd go with the Smart Tag PLUS version (which can use an additional network, still powered by Samsung, but not just by their phones). In any case, they should still be cheaper than Apple's and work better with an Android device. Similarly, Tile sells 'device-agnostic' tags... They are, after all, the ones that made tags popular.