LjL: I started reading your question and got confused because I think you're comparing number of occurrences over 2 months with number of occurrences over 1 year. Anyway, now I'm doing my own math.

1) The upper bound on natural occurrence of 30 Bell's Palsy (BP) per 100k people (p) per year (y) is nat = 0.0003 BP/p*y.

2) Recorded in the vaccine group were 4 occurrences over 2 months (that's the median, really we need the average but that's not reported anywhere). This is for roughly half of 37,586 participants, so I get vac = 4 BP / (1/6 y) / (37586/2 p) = 0.0013 BP/p*y.

Putting things together, we get vac = 4.3 nat. That's 4.3 times the upper bound so I'd say you can hardly call that "consistent with the expected background rate in the general population", don't you think? Did I do the math wrong?