We realize that this is an uphill battle if there ever was one. After all, the tail wag has equaled "happy" for so long, it is hard to accept it as anything but that; it is an association deeply ingrained in human nature.
And yeah, it might be that. But don't assume that a strange dog is friendly just because it seems to be doing its best to achieve liftoff with the sheer force of its tailspin. There's a chance that could be its way of frantically screaming "Fuuuuuuuuck oooooofffffff!" at the top of its lungs while somehow simultaneously flipping you off with all paws at once.
The tail can send a bunch of different emotional signals, depending on the kind of wag. For instance, look at the height of the tail -- if Spot is holding his tail up high, he's warning you. The motion is meant to be seen from far away, so it's kind of the equivalent of raising his voice ("Yeah, there's a big badass dog over here, back that s**t off, son!"). If the tail is a little lower, he's more calm. If he's keeping it down near the "between the legs" position, he's scared.
Then you also have to consider the direction of the wag. A dog wagging its tail more to the right has noticed something it is cool with and would like to approach. However, if the wagging is switched to the left, it indicates anxiety. All of these nuances of wagging can convey a wide spectrum of different emotions to other dogs from a safe distance. So, yeah, a simple switch of direction can change your dog's message from a loving "yo, I love you, dawg" to a frantic "your stupid monkey face is literally stressing me out, you revolting butt. Come closer and I might freak out."