There is no certification in FBAs, though you could assure training by asking for a BCBA. It should be done by a person with specific training in behavior assessment, though, with or without the BCBA. In most buildings, that would be the SP. In some places, there may be a BCBA who is not also the SP.
One of the complications is that anyone can do a classroom observation, but that doesn't necessarily mean they are observing with intelligence. A good FBA should minimally have interviews or surveys of behavior from multiple sources, including parents, a well-defined/operationalized set of target behaviors, and direct or indirect assessment to identify the antecedents, consequences, and functions of behavior. I usually conduct multiple classroom observations, at various times of day, during different instructional settings, with various staff, and across many days. I also prefer time-sampling behavior, with a non-referred comparison peer, as I love data. There is no FBA that should conclude that the child is "fine." The outcome should identify the four elements listed above (antecedent-behavior-consequence and function of behavior). Someone saw a pattern of behavior of some kind, or there would be no referral. One could conclude that it was setting specific, and thus not observed at that time, or that it was a singularity, arising from a low-frequency set of setting events.
If your FBA does not clearly indicate ABC and function, then it is not an adequate assessment. In the event that the observer can document a plethora of observations, without any sighting of the target behavior, then that, at least should be supported with data. (E.g., time samplings, with the target behavior occurring in 0 out of 150 rated intervals, observed in five sessions, across three days and four settings.)
It sounds like your observer did not see the behavior at all, probably because it resulted from bullying, and the aggressors were smart enough not to do it right in front of the teacher. That's why I interview the student, too, and try to observe as unobtrusively as possible when I'm in the classroom, cafeteria, or on the playground.
