That Muslim sailors could have reached the American continent in the 12th c. isn't implausible, but Erdoğan fails to take into account it that that's still almost 200 years after Eric the Red first landed in the New World, an event with archaeological support (L'Anse aux Meadows).
I've found a creative interpretation of history in conversations with Muslim friends (those born and raised in the near and middle east) over the years. One day, years ago, my roommate at the time, a Moroccan, made the claim that Morocco had never been colonized like the rest of Africa. Given that we were having this conversation in France, it would have been easy to bring up the partition of Morocco between Spain and France early in the 20th c., but I decided to rebuke that by starting with the Romans. Mauretania's status as a client kingdom was ended by Claudius in AD 43, and it remained a Roman province for the next 400 years. But the Romans, Vandals and Visigoths wouldn't count, I realized, because these events occurred before Islam came to Morocco, so that didn't happen to Morocco as he envisaged it. OK, I accepted that, as many European countries have the date of Christianization as an historical event of major import.
So... then I brought up the fact that he grew up speaking a language that originated thousands of km from his hometown and worshipped a religion that was brought to his country at the point of a lance. He didn't see it that way, and as he told me how he'd been taught in school about what we non-Muslim non-Moroccans would see as the Arab conquest, I realized he saw the arrival of Islam and the Arabs in about the same way the Irish see St. Patrick, as if the Arabs were cassocked monks peacefully spreading the word of Allah. I even tried explaining to him how proud as a Muslim of Arab descent he should be of the real story of the spread of Islam, how extraordinary a feat it was for the Arabs to manage, in the space of 100 years, to conquer more than half the known World, from the Indus to the Pyrenees, defeating two of the three strongest Empires on Earth at the time in the process; how amazing it was that in most cases, the Arabs didn't force people to convert (as the Europeans did in the New World) but respected the Peoples of the Book and encouraged conversion through taxation and social policy. It didn't phase him: he had his story and he was sticking with it.
This anecdote isn't meant to be authoritative. I'm also not denying that western Christian countries don't also pick and choose the history they wish to highlight, but from my experience, history is very malleable as taught in the Arab world where even epic triumphs can be explained away to fit a narrative