Because Hogwarts accepted only students from the British Isles, refusing even foreign students from mainland Europe who wished to study at Hogwarts because of Albus Dumbledore's reputation, Credence, far away in North America, could not attend Hogwarts.
This was not simply because owls could not cross the Atlantic Ocean like migratory birds. Hogwarts' admission list was determined by the Quill of Acceptance and the Book of Admittance, whose range of perception was probably limited to the British Isles. If the headmaster or governors "artificially" added the name of a new student not on that list, it would create a "loophole." Parents unwilling to admit that their children were Squibs would try every possible way to send them to school. As long as they got in, it would prove their children were not Squibs.
Credence's real name was Aurelius Dumbledore. That name had once appeared in the Book of Admittance, but as he became parasitized by an Obscurus, it gradually vanished from the list, because the nature of an Obscurus was to devour a young wizard's "aura."
Squibs also had an "aura" at first, but it gradually faded away on its own. When it became too weak for the Book of Admittance to identify as "sufficient evidence," even if the Quill of Acceptance sensed it, it would not permit the name to be written on its pages.
Being "eaten" by an Obscurus was another matter. Aurelius was the name of a Roman emperor and Stoic philosopher. This school believed that the universe was a beautiful, orderly, perfect whole, evolved from a primordial divine Spark. Humans were part of the cosmic system, a small spark. Therefore, people should bring themselves into harmony with the greater direction of the universe.
Unfortunately, the "small spark" did not turn out as Credence's parents had hoped.