It is true that you can form 6.5/06 and 6.5/06AI (among others) from either .25/06 or 270. Just two critical details to mind carefully. First, make sure your length of your re-sized brass is appropriate. 270 will end up too long and 25/06 ends up short. Second, check the neck diameter of your finished round neck against your chamber diameter and turn down or ream out to get safe clearance and neck tension, if needed. One of my rifles has a .297" chamber neck and my friend I shoot with has a rifle with a .301" chamber neck. His finished rounds will not chamber in my rifle, but mine will chamber in his. He can just neck down, trim for length and load up. I have to do the extra step of reaming the neck material. You can form brass with the 6.5/06AI die and then fire form to the chamber. I prefer using 270 brass in my rifle as I find it is easier to size it down, trim for correct length and fire form with the bullet seated normally.
Using expanded and fire formed 25/06 brass in my rifle usually ends up at 2.476"-2.480" before firie forming and needs to have the bullet seated touching the lands to get the shoulder to fully form with the correct headspace. That's a lot of brass to flow and stretch so usually I only get two or three loadings.