I totally understand the whole 'don't jump at ghosts' thing, but my family has been bitten by that many 'ghosts' (aka theoretically very unlikely occurrences) that we know better than to dismiss them now.
Someone mentioned there is no horizontal transmission from vaccinated birds to unvaccinated birds in the case of neither being exposed, as per the claim made by that poultry site, but I've read that there is some degree of it, on a few sites now (research ones, not layperson ones, lol)...
I'm off to bed now so won't spam some links, but here's some info:
This might be seen as 'jumping at ghosts' but personal experience has led me to take things overall with a bit more seriousness; if there is a possibility, almost no matter how slight, I bear it in mind. Failure to do so has brought us undone so many times now, I guess I probably am a bit sensitized to low probabilities. They've never been as low as we were counting on them being, lol!
Bit of random further reading for those interested:
Best wishes.