You're right, that's different, but it can also be foiled, at least in theory: you just have your cellphone add some time delay before responding. The delay could be different for each cell tower.
I realize that's a big ask (and is probably something the operating system can't do), but it doesn't violate any laws of physics.
Generally, each base station within range receives all messages from your phone. Even if you were to address different messages (with different response delays) to each station, they would all still "see" the other messages. They then record that message (or an identifier - akin to a TCP sequence number) and compare the (synchronised) time at which this message was received. This is used to calculate the difference (thus delay) of each tower's reception of that message.
I don't think what you're suggesting would actually work given the way mobile network infrastructure works (where multiple cell base stations may see each message at the same time).
I'd be wary of how this would affect call quality - if you were adding delays to sending call data to the tower you might end up with a laggy/glitchy phone call.
How often are you really on calls, though? Assuming this would be feasible, you could just have it turned off whenever you are not on calls or whenever you don't need your phone to tell you your location.
I'm not really sure it's feasible, though. I don't know the details of how phones interact with towers, but I would think that what's happening is that your phone broadcasts a radio signal, and that same exact signal is picked up by more than one tower. If you want to triangulate the location of the radio signal, you don't need to know how long it took to get to the tower, you just need to know how much longer it took to get to one tower than the other, and the locations of the two towers.
Additionally, I think you can make a similar calculation based on signal strength if you can account for anisotropies in the attenuation of the signal. This seems less reliable to me, but if this is how it is done you could potentially throw off your location by a little bit by putting your phone in a partially shielded case that increases the attenuation on one side relative to another.
