But Siac ruled Jordan had not proved Abu Qatada's retrial would be free of evidence obtained by torture.
The European Court of Human Rights said that if he were deported, Jordan might use evidence obtained by torture.
Jordan has agreed to change its law to ensure that no evidence obtained by torture could be used in his case.
The ECHR had previously blocked his deportation to Jordan, unless assurances were made that evidence obtained through torture would not be used in court.
The home secretary's lawyers emphasised the Jordanians have enshrined into their constitution an "express prohibition on the admissibility of evidence obtained as a result of torture".
Angered by this new evidence obtained by the Standards Committee, Philip Davies, the Conservative MP for Shipley in West Yorkshire, demanded the police reopen its investigation.
However, the Court of Appeal concluded SIAC had misdirected itself in law and its decision could not stand because of the issue of evidence obtained by torture in Jordan.
The process has been roundly criticized by defense lawyers, who are fighting to keep hearsay statements and evidence obtained through coercive interrogation techniques from being used against their clients.
Last July the president authorized evidence obtained through torture.
At the Court of Criminal Appeal hearing in Edinburgh, the Crown conceded that without the evidence obtained when Mr Chamberlain-Davidson was first interviewed, there would not have been enough to convict him.
Last month the Special Immigration Appeals Commission ruled it was not satisfied the preacher would be tried fairly in Jordan because the case could include evidence obtained by torturing his former co-defendants.
But the evidence obtained in this way has been less compelling or complete than that given by people seeking amnesty, who must therefore tell (or at least seem to tell) the full story.
The interpretation of the evidence obtained in this study, based on the use of advanced analytical methods, supports the hypothesis of an intentional therapeutic treatment, but alternative post-mortem practices are not ruled out.
In November 2012 Abu Qatada was released from prison once more after a UK court backed his appeal on the grounds that witness evidence obtained by torture could be used against him at trial in Jordan.
BBC: Abu Qatada case: UK agrees assistance treaty with Jordan
At issue in the appeal was whether he had constitutional protection as a lawmaker, so that evidence obtained in that search should not have been presented to the grand jury to obtain the indictment.
"Although there appears to have been an incident on the evening in question, evidence obtained from witnesses contained multiple inconsistencies and there is insufficient evidence that Mr Joyce committed any offence, " a CPS spokesman said.
President-elect Obama has suggested using the normal US legal system to try them, but some of the evidence available under the military commissions (evidence obtained by coercion or worse) would be banned from US courts.
Last month, a senior judge ruled Jordan had not proved that the retrial of Abu Qatada - who is currently living under strict bail conditions in London - would be free of evidence obtained by torture.
Last November, the Siac ruled there was a risk that evidence obtained by torturing witnesses would be used against him at his retrial in Jordan - meaning that he would not get a fair hearing.
In January 2012, the European Court of Human Rights blocked Britain from sending him to Jordan because of fears that evidence obtained by torture could be used against him at the trial planned by the Middle Eastern country.
CNN: UK loses latest attempt to deport radical cleric Abu Qatada
The Special Immigration Appeals Commission (Siac), which adjudicates on national security-related deportations, ruled last year that Abu Qatada should not be removed from the UK because his retrial could be tainted by evidence obtained by torturing the cleric's former co-defendants.
BBC: Abu Qatada case: UK agrees assistance treaty with Jordan
Before Italy's election this May, lawyers for defendants in each of the three cases of alleged bribery of judges, in two of which Mr Berlusconi is involved, challenged the admissibility of evidence obtained by Italian prosecutors from their Swiss counterparts.
Ministers want Abu Qatada - who British judges have described as "truly dangerous" - to stay in jail while diplomats try to strike a new deal with Jordan which would satisfy the European Court that the 51-year-old would not be tried on evidence obtained from torture.
This would apply not only to evidence directly obtained under the convention, but also to any oral testimony derived from that evidence.
These include the way in which identification evidence was obtained from a Maltese shopkeeper, Tony Gauci.
Unlike ordinary American courts, the commissions can admit as evidence information obtained through coercion (but not torture).
"During the criminal investigation, evidence was obtained including positive tests for the presence of anabolic steroids and other performance-enhancing substances for Bonds and other athletes, " the indictment reads.
The inquiry, which was completed by Hampshire Police on Thursday, was triggered by Warren's unsuccessful appeal, in which he argued key evidence was obtained by the illegal bugging of a car.
In any event, no actual case has been identified where the government would be precluded from obtaining a conviction against a known al Qaeda operative because most of the significant evidence was obtained through torture.
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