"Chickens aren't people, and they don't mind drinking out of water with a little dirt in it--or eating garbage off the ground, or pooping in their house. They'll drink out of puddles and crap in their food tray, for God's sake. Even the occasional bit of green algae on the inside of the waterer...
Using a metal tablespoon is just fine. Your answer to the reason no metal and vinegar is right on. It is the overall acidic reaction to the metals, but that takes much more exposure time than a few seconds.
Coming from a gardener's stand point and only a newbie at having chickens, I don't think the chickens would be a good control for the squash bugs. They really multiply quickly, hang on under the leaves and in little folds, and when first hatched, are really, really little. I've always had to...