Reminds me of the movie Gumball Rally, the original, when the Italian driver in the Ferrari rips off the rear view mirror and says, "What is behind me is not important".
A lot of truth to that in racing but definitely not on a bike path. My view may veer from previous posts but since you had 100% visibility of the rider in front of you, and the rider in front of you did not have good visibility of you, in my opinion it is on you to slow down or stop if you don't know which way the rider was going to go. The "better safe than sorry" mantra.
My acid test if I'm on a bike path, very seldom, is I pretend the people walking, running or riding in front of my are very elderly in the 80's or even 90's. People that age don't react quickly, may not hear much of anything, might get confused and well, it's my OBLIGATION to look out for them. I will generally come to a complete stop unless I DO see a signal.