> that had a real, legitimate excuse attached to them
So, in your opinion you believe that you as a TA have the right to know the personal details of students' lives if they need extensions? What if the matter is private?
If you don't want to tell me anything about why you want an extension, you have to accept the fact that the probability distribution over "I want an extension" absent any information is heavily weighted toward "I went on a bender and am too stupid to stay in school", and as such I was unlikely to say yes. I don't want details details; but "I broke my leg, this, this and this is going to be a week late, I'm sorry" as happened to a friend of mine is perfectly good.