Tinfoil hats aside, we’re conflating a few things here.
Your phone – all mobile phones – are trackable by your phone company in so far as the phone mast knows what’s connected to it at any given time. With signal strength and triangulation with other masts it’s possible to tell where your phone is to a vague degree of accuracy, depending on mast density in the area (so more accurate in city centres, sub-100m I believe). Whether the phone company records this data or not is (I assume) down to them, but I can’t see a compelling reason not to. It’d be useful information for, as a random example, the emergency services. Or legal issues.
Your smartphone is probably equipped with a GPS receiver and so will know with pretty high accuracy where it is whilst this is enabled. It can also use the Wi-Fi signal to hazard a “coarse” guess based on the hotspots and suchlike it can see. This is how your location profile is built, and what is sent Google ( / Apple / Microsoft) if you enable Location Reporting.
Location History is something else again. Enabling this is what makes your maps history and things like Google Now work. Assuming you believe Google (and if you don’t then you’ve seriously wasted your money on a phone), if you delete your history then that data is gone for good. So there’s nothing to stop you from enabling Reporting but not History if you so desire.