There are many rights called out specifically as "natural rights" or "God-given rights" but your ability to access a data store that is not yours isn't one of them, nor is it among the unenumerated rights alluded to in the U.S. Constitution.
Chrome may be misbehaving. Chrome may be detecting that you have a video downloader plugin and blocking you. Perhaps... Don't use Chrome. I personally recommend Firefox. But one thing Chrome, Google, and YouTube are not doing is infringing upon your rights.
Sure, but you are getting off the course. The ability of a company to know what is installed on my hardware and decide based on this information what to do with it, much broader topic then the access to a storage with a third party content on it.