As Andrew says you probably need a 10mm or maybe even 8mm shank tool to bore a 13mm hole.
The reason that the common tips don't have much clearance is that the edge would be too fragile and chip easily.
You will find that as the bar dia gets smaller the angle that the tip is held at increases to give as much clearance as possible

3 Flats is unusual for alathe boring bar, can you post a picture as it may be meant for aboring head. If you do want to rotate it then make or buy something like this that is bored to fit the round of your bar
Edited By JasonB on 28/06/2016 19:01:49