You are right and I really don't think people are holding YOU responsible. I don't. I know that your mom is the adult in the equation and its her decision. Growing up myself we had an outside dog. He was never tied tho. He had full run of the 3 acres of my parents place. And a doggie door and nice warm dog house with lots of blankets in it to keep him warm in the winter and in the summer HE pulled the blankets out. He really had it good in there in the summer b/c we didn't have a/c at the time and it was cooler in the garage the our house. The people here are just frustrated with the situations and uneducation of people like your mom that makes the animal live in this situation.
And just b/c lots of dogs around where you live have that kind of life doesn't make it right or doesn't make it better for people to accept. A lot of dogs around here are like that too and it still pi$$es me off.
That said there are a TON of outside cats also and it still irks me also.