The judgment said part of the reason that Rolls secured a DPA was that management at the time of the bribery had been cleared out and that Rolls was a different company now.
Had it faced criminal charges, Rolls could have been banned from doing business in many countries, wiping out a huge chunk of its £75bn order book.
Sir John led the FTSE 100 company from 1996 to 2011, a period when several of the offences took place.
Lord Justice Leveson's judgment said Rolls knew about corruption claims in 2010 but did not inform anti-graft regulators.
Being questioned under caution would have involved Sir John's being read his rights, and is a different process from the SFO's questioning of witnesses.
Sir John is not the only person to have been questioned under caution, and it is understood that "dozens" of those involved at all levels have been quizzed.
Sir John, who is being represented by law firm Wilmer Hales, has denied any wrongdoing.
An SFO spokesman said: "We cannot comment on an ongoing investigation."