Well, there is a difference between what most players consider random and what the physics of the world considers random (Otherwise known as actually random, regardless of whether the randomness has been an asshole to anyone):
Physics/Math/Mother Nature/The Universe considers something to be truly random when all things have an equal chance of being selected in the process. As long as that condition is fulfilled, it doesn't give a metric f**kton about what the actual results are. It only cares whether the process is random or not, and so, if you get sixty-two 1's in a row, as long as the process is random, those results are "random".
However, players like you or I cannot understand, nor observe, nor visualize the process of choosing a random number. Therefore, we can only base our observations on the results we get, and we must recognize that what we use to determine randomness and what true randomness is are not the same two things, and, at times, what seems to not be random is actually random, however counter-intuitive. If we get the aforementioned sixty-two 1's in a row, we cannot see the process of choosing those sixty-two 1's, and therefore don't know if it's random or not, and it could be and could be not, but we can't just say "It's rigged" or "There may exist a bias somewhere in the process" until we observe the process for ourselves. Of course, about 0 people here want to drive over to random.org's HQ and hear atmospheric noise for days on end, so we can only trust that it's random. And so far, due to the LLN (Law of Large Numbers), it has been shown to most likely be random.