Is it true that most linguists assert Basque has not substantially changed?

Not to my knowledge. The late Larry Trask, preeminent vasconist of his time, spent a lot of leisure time refuting inane claims about Basque being related to every language on earth, and part of his armoury as a historical linguist was that such inane efforts made use of modern Basque dictionaries, whereas​ both what we have reconstructed of proto-Basque, and what little we know of Aquitanian, the ancestor of Basque, are phonologically different.