Yes children of today should definitely be allowed to watch unmonitored television . I would lije qoute an example before beginning with my argument. It was afternoon and I was watching television. My mom walked and say what I was watching and finding it inappropriate for me to watch she told me to change the channel then got busy with some work. I switched it on again. Is this monitoring sufficient ofcourse not. Hence what is required is monitoring our values and morals and bringing them up in such way that our conscious doesn't allow us to watch anything that we shouldn't. We must be allowed to take decisions for ourselves.
This argument surely should offer some sort of compromise. It example is unclear as you do say yourself that the television you were watching was 'inappropriate' this means that it was NOT something that you should be watching. It almost seems that you are almost in a different motion, about freedom and discovery of choice. Perhaps the real solution is not about conscious yet about building a well established relationship between parents and children which promotes honesty. It is possible that your parent went about the wrong way of making a decision.