I see this as really simple. "On your left" means exactly what the person hearing it perceives it to mean. Nothing else matters. He or she will react according to that perception. What the term "really" means, here, in legal code or anywhere else matters zero (at least not until this comes before a judge and long after the crash).

I try to call out "on your left" on more often "bicycle behind" or just "bicycle" with no expectation as to what this person is going to do. (I sometimes assume. Sometimes I assume wrong.)

Ben