No, they say they can't really know. But the pre-eminent Assyriologist, Dr. Simo Parpola, says we are. But it doesn't matter, no one can question our ethnicity: http://assyriafoundation.org/modern_history.html
From Nick AlJeloo?s ?Who are the Assyrians??, The Assyrian Australian Academic Society:
The Assyrian nation, apart from undergoing an ongoing genocide, has also suffered a cultural genocide that has attacked the Assyrian identity and questioned its origins and unity as a people. Assyrians have come to be called Nestorians, Chaldeans, Jacobites, Syriacs, Syrians, Maronites and Melkites through religious influences and by the governments that now rule over portions of what is their ancestral homeland. As esteemed social anthropologist Dr. Arian Ishaya of UCLA in her paper Intellectual Domination and the Assyrians states, there are different ways of dominating a people, those most direct being to take hold of their land and resources, deny them statehood, and force their manpower to do the labour work or fight the battles of the conqueror. But she also mentions that domination may also come in a more indirect, abstract form which is intellectual, this form being the most dangerous as it penetrates the victim?s inner feelings and thoughts. Thus, she determines, the victim remains unaware and willingly subjugates itself to intellectual domination.
?The Assyrians call themselves and other people of Aramaic-speaking heritage Assyrians for a very simple and convincing reason: they are the age-old inhabitants of ancient Assyria. It is their homeland. They have churches there that date as far back as third and fourth century AD and still others, such as St. Mary at Kharput and St. Mary at Urmia, that are of apostolic foundation. That is sufficient and says it all. There is no need to engage in the inconclusive argument of racial and cultural purity. When any nation says that it is what it is, it is that because its forefathers inhabited that region since time immemorial. The Assyrians say they are Assyrians because their forefathers inhabited Assyria and the French say that France is their homeland because they have lived there for many centuries. One claim is as valid as the other. What makes the French claim more respectable and that of the Assyrians questionable isn?t science. It is politics pure and simple. Thus, Dr. Ishaya concludes, ? ? the question of whether the contemporary Assyrians are Assyrians, should never be asked. When a scholar makes that a topic of research, he is playing POLITICAL GAME in the guise of science. There is no excuse for the academics to remain naive any longer. The scholars have no choice but to decide what they want to do with their profession: put it in the service of the people or use it to promote the interest of the ruling powers. Whatever choice they make, they can be sure that they can no longer fool the people.?