You are exactly right in assessing my answer. I'm quite sure that venison or any meat will not become "poisonous"  as a result on extended freezing but as I said toward the end of my answer "venison cannot be frozen indefinitely and retain any degree of quality."
    Quality is sometimes like beauty and tends to be judged by the eye of the beholder. If you read through the FAQ's you may have run into the guy that broke out in a rash when eating old venison and he still didn't want to throw it away! Another found a dead deer in the woods (not during any season) and wanted to know if the meat was salvageable. Others have had freezers go out, hung deer for extended periods in warm weather, gut shot them and not rinse them out, etc, etc, Then they would like me to give a green light to eating the meat which I cannot do as a matter of principle and common sense.
    If you feel that 3 year old hamburger  agrees with your standards then by all means go ahead and use it. However as for myself and the food safety experts and home economists  that I've read recommendations from on freezing meat, I would throw out burger that old and start over.     
    Good Luck,

Dave