Yoga a religious practice?

We have often said firmly that yoga can be practised without a belief in Hinduism. One, because yoga is a set of exercises, and two, if the sound and postures that are required to be adopted a notion of Hindu mantras or postures to someone, he/ she can modify it to suit one's liking or leave that aside.
We came to see a video that demystifies Hinduism in a very brief discourse. You may like to have a look at it, not for yoga sake but to appreciate that a true Hindu won't mind praying to 'your' or 'his/ her' god. The video is at youtube, linked below:
http://www.youtube.com/watch?v=e-mTwKQolLM