the notion of indirect deduction of proof from inference in the eyes of the sahaaba

A narration via Abu M`amar rahimahullah asking Khabbab ibn Arat radhiallahu `anhu regarding how would they be sure if the prophet sallalahu `alayhi wa sallam would recite anything in the prayers of dhuhr and `asr? 

The sahaabi radhiallahu `anhu said : WE (plural) used to make that out (i.e. infer it) by seeing the beard of the prophet move (so we understood he was reciting ) 

[Ref: Sahih Bukhaari , Kitabul Adhan 761] 

this is a good proof to use for the science of inference and as is known the scholars or even humans since time immemorial have used the notion of inference to establish many customs, actions, laws and more. 

Some may argue what is the indirect inference here? Well the mere moving of the beard could be for many reasons because the prophet sallalahu `alayhi wa sallam in the past has proven to the sahaaba how he can see them even from his back side or how angels rushed to write down a particular hamd said by a sahaabi after getting up from rukoo` or how he saw jannah or naar at times during his prayers/du`a. Or he could be speaking to an angel but the sahaaba and taba`een used this inference specifically to deduce the proof of reciting surah fatiha + surah during dhuhr and `asr.