I did talk to the vet and they say it can happen from stress, especially if you have to chase the bird around in a big cage, having problems catching it. Also of course it's important not to apply preassure to the chest when holding it, and be as quick as can be about it.
They also said there is always a risk giving birds medication as you never really can tell the reaction from it. I think Mr. Winterbottom is feeling a lot better though, he is a lot more active, and he sure looks better.
I think the fainting issue came from stress of being caught and held. Hopefully it will not happen again, it went a lot better yesteraday when we gave him his medicine.