We need to import multiple youtube videos for each product and display them nicely as thumbnails or links that open in modal window on product page. It seems that none of the product video extensions support importing videos.
That's because youtube doesn't allow it. Read terms of service, section 5.1. A through D all say pretty much the same thing: can't use / copy. Youtube has ample documentation about how to embed their player into your site. For that you don't need to import anything.
I read the terms and you have been mistaken. There is no such clause that prevents me to import youtube embedding codes to our site. It just states that you have to use the youtube provided method to show the videos and using the embedding code is that kind of method.