The tiles themselves do not, as far as I am aware, have GPS. I use Tile to keep track of a few valuables (and it actually does work), and you do need an account with Tile. Each Tile has some sort of unique identifier that it transmits over Bluetooth to the nearest BLE device with the Tile app on it. As long as that device has GPS on it, it will pick up the BLE connection, and send the identifier, together with the device's own GPS co-ordinates to the Tile servers, which will then look up the account of the person who owns the Tile that the app just found.
The person running the app that found the tile does not get access to it. Indeed, the app does not even tell them it's done anything.
Don't want it reporting your location to Tile. Fine. Carry on as you are. The system will still work as long as enough people in an area do have it.
As for power usage, it's not actually that much. The Tiles themselves last a year on a single CR2032.
I do use Tile. It's handy in case I lose my keys, and I use it to track my backpack which often contains a £800 laptop..
I can understand the security concerns. Despite being an iPhone user, I am also a System Administrator, and well aware of the problem of security. As a rule, I do lock things down as far as I can, but the old computer security adage (Security, functionality, features: Pick two) applies. I prefer the extra functionality of it being easier to find my keys or backpack than the slight security risk of keeping Bluetooth enabled.