dodleraspoon there is no telling how someone wired the switches. You see some crazy things in homes sometimes. It sounds lie it might be right though.
Here is a bad drawing of a three way switch wiring. I kept it simple by leaving out the neutral and ground wires. The neutral and ground just follow the hot wires to the light to give it a ground and the current a return path to the panel on the neutral.
power comes in on the black screw on one of the switches and then the black and red in the 14/3 alternate the current depending on how the switches are positioned to the other switch at the end of the hall or stairs.
The black screw on the other switch takes the power to the light.
A three way switch just alternates the current from the black screw to one of the brass screws as you flip a switch. Say the switch is up, then the power goes to one of the brass screws and then flip the switch down and it takes power away from that brass screw and makes the other one hot.
You need to get power to your new light from either the switch that feeds the light or from the existing light. Don't forget to connect the neutral and ground.
I hope this helps more than confuses you more. If I didn't explain something well enough email me ( get address from my website or from here)and I will explain more.