It is possible but not necessarily probable. The annulment process is purposely detailed and the burden of proof high. The presumption at the beginning of an annulment process is that the marriage is indeed valid, the burden of proof is on the petitioner to prove that the marriage was invalid for a specific reason (canon 1060). This is not a simple weighing the evidence pro and con but rather an annulment requires, essentially, proving beyond a reasonable doubt that the marriage was invalid.
Obviously limited human beings are involved so there is always the possibility of an honest error or mistake. That is why every decision must be approved by a second tribunal. But, yes, it is *possible *that two tribunals could innocently reach an incorrect decision in favor of annulment.
However if someone purposely mislead or lied to the tribunal to attain their annulment then they would be guilty of a grave sin. If both sets of judges for an annulment were purposely lax or sloppy then they too would have to answer to God for their derelict of duty.
