I have done dozens of surveys that use my web cam; but the difference is that I've always known up front within the first few qualifying screens that I was going to be asked to use my web cam. They have all been quick and easy and paid with no issues. But just because *I* don't have a problem with it doesn't mean that it is for everyone. So I agree with the op's frustration with having that sprung on her that deep into the survey. If it were me, I likely would have gone ahead at that point and granted access. But that's just me.
On a similar note - I hate the surveys that ask me about my kids and then ask if my child is available to take part of the survey. Depending on the survey topic, I don't have a problem with this (provided that I am IN THE ROOM with her and see the questions that they ask) and have let her participate in several surveys. The part that I dislike is when they don't inform you up front that they are going to ask you to do that. I've had to suspend (and lose) quite a few of those because my child was unavailable at the time.