The Mishna in Yoma says that when the Kohen Gadol used to read from the Sefer Torah on Yom Kippur, he had to read two portions: one from Acharei Mos and the other from Emor. It says that he used to read Acharei Mos, then he used to say the reading from Emor by heart.
The Rambam explains that he couldn't
- Roll it to Emor - since it wouldn't be Kavod Hatzibur to have them stand and wait for the Kohen to roll the Sefer Torah.
- Read from another Torah - since it could cause people to suspect the first one to be not kosher.
So the Kohen had no choice but to read a portion of the Torah by heart (which is a generally prohibited).
Nowadays, we take out two Torahs whenever there are two readings in one day. Why are we not concerned for the honor of the first one?