There's a lot of ways to signal this.
With a left turn arrow, that should never be green when the turn conflicts with a pedestrian crossing that's on Walk. An arrow is an indicationn of a protected turn, where there should not be any conflicts.
But many intersections allow for an unprotected left turn, if safe, on a green ball in the forward direction. Sometimes there's a green and yellow arrow next to a green and yellow ball, with red on top in the middle of the two: you can usually make an unprotected left, if safe, if the green ball is showing, and if you have a green arrow, it's a protected left. I've also seen similar with a flashing yellow arrow indicating an unprotected left is permitted, if safe.
Of course, it's possible that the intersection was miswired or misconfigured. If the direction with the green arrow also had a green ball for forward, it may have been that the right side of that direction was supposed to have a Walk, but the signals were tragically misconfigured. I have experienced a case where wires were mixed up, but in the case I'm aware of, a bike button was configured as a left turn occupancy detector for another approach; inconvenient, but not dangerous.