It says in Aruch Hashulchan1 That we tried all positions, Sitting by Krias Shema, Standing by Amidah, and Fall on one's face during Tachanun.
So then we say ואנחנו לא נדע...מה נעשה "We do not know (what other position to do)... what should we do."
So my question is, if this is one of the reasons why you "fall down on your face" during Tachnun is because we try to do all positions.
So why does it depend on if there is a Sefer Torah or not? You should always do it, in order to try all positions.
1 (in O.C. 131, 9)