The debate is because of the 1916 New York Giants season in which they won 26 games in a row, but there was a tie in the middle. Whether Indians fans what to hear this or not, Cleveland 19 asked for an received the official statement from Major League Baseball.
The second longest streak in MLB is held by the 1935 Chicago Cubs winning 21 in a row. Meaning according to MLB the Indians have ties the second longest streak.
Here is what happened 101 years ago to create such a heated debate. First take a look at the schedule of the Giants to get some perspective as provided to Cleveland 19 by MLB and Elias.
On September 18, 1916 the Giants played a double header against Pittsburgh. The second game ran late into the day and had to be called because of darkness. Remember in 1916 there are no lights. The first night game wouldn't happen for another 19 years in 1935 in Cincinnati. The game was actually very close to completion when it was called. On the stat sheet you can see the game had been played for one hour and 24 minutes. Hall of Famer Honus Wagner had a the game-tying RBI in the eighth inning. The game was nearly complete. Just before the Giants we headed to bat in the bottom of the ninth inning the game was called due to darkness.
In 1916, the rule was any game called due to weather or darkness was just scrapped. It wasn't suspended, picked up where they left off and completed the next day, like it is today. The rule was the whole game was scrapped and started all over again.
That's why on the stat sheet above you can see another double header was played the next day on September 19, 1916. The first game of that double header would have been the make up game of the previous days tie. The Giants won that game 9-2, and the second game 5-1. They would go on to win a total of 26 in a row.