I think a lot of the problems with mangled screws, Torx, Phillips, Hex, Etc. is caused by dirt in the recess which prevents the driver from full engagement. Even when the dirt is finally cleaned out, the upper section of the recess has been rounded so there is now less surface area for the tool to grip. I see this happen so often and think when are folk going to learn, clean the dammed recess first.
Having said all of that, I do think that the recess in the Torx screws the Blue Heeler is referring to are often very shallow.
With the tool well supported, try using a small punch to hammer the screw head into shape, the lots of downward pressure whilst turning.
Just my two pennys worth.