My wife bought some office furniture some years ago and I was pressed into service assembling it. The screws were button head with 5mm hex sockets. Each chair had a 5mm Allen wrench in the fastener packet and I was barley able to keep ahead of the wrenches as I assembled the ten chairs. "Lousy tools" I thought. When the assembly was done, A had a collection of 5mm wrenches. I decided to to a little experiment. I heated the wrench to a cherry red, until tit was no longer magnetic , then quenched in water. I polished the wrench to a bright finish and heated it slowly from the middle until I had a dark straw color at the business end. Guess what? It is now hard to a file and no longer twists in use.
Nothing wrong with the steel; they just do not know how to harden and temper.
Back to the original issue: bending drill bits. I have observed this when hand drilling because the drill spindle is not aligned with the hole being drilled. It usually precedes a snapped drill bit. Is it possible that the spindle is not aligned with the quill so the drill is being fed off axis? On a lathe, this would be indicative of a misaligned tailstock.