In Eretz Yisrael on the first day of Chol HaMoed (just mentioning this to say where it happened) 2 Sifrei Torah were taken out for Krias HaTorah. They put one Sefer down on the bima and the other was held by someone on a bench behind the bima. They opened up the Sefer Torah and realized it was the one that should be read from 2nd, not first. They asked someone there who is a Rov what to do and he said to roll this one to the right place and read from it instead of bringing up the 2nd one that was already rolled to the right place.
What is the source for this? If both Sifrei Torah were already taken out why can't the one on the bima be switched with the one on the bentch? Seemingly if we already have a Sefer Torah out of the Aron Kodesh that is ready to be read from better perhaps then "bothering" the tzibbur by rolling the Sefer Torah to the proper place. As well perhaps this is not going to be a problem of thinking there is a pagum in the Sefer Torah when they are already both out.
Update: While I don't think this would be done practically. However in such a case why can't first the reading of what is really the "2nd" Sefer Torah be done before the normal reading of the day (which is in the first Sefer Torah.)