You're out in the yard and you see a distressing sight – a baby bird is floundering around on the ground, looking like it's desperate to get in the air, but it can't despite all its efforts. Suddenly, out of your peripherals, you spot a cat readying for a pounce. Sacre bleu! You rush over to scoop up the little bundle of feathers, take it into the house, and try to remember how to assemble a shoebox nest to serve as a habitat for your precious little find. You'll raise it yourself until it's ready to fly.
While this is wrong on several levels, it's not because you touched the bird.
Baby birds usually don't leave the nest until they're ready (or at least readyish) to fly. But, just like how well you drove during your very first driving lesson, they typically stink at flying at first. So needless to say, they suffer a few false starts and end up on the ground, whining like a teenager who wants the keys but hasn't completely got the hang of which is the gas and which is the brake.
But that doesn't mean the fledgling's parents aren't supervising their offspring. They're probably in a nearby tree, shuddering as their little dunce forgets all the lessons they taught it. And if you leave the baby bird alone, chances are they'll be there soon to smack it upside the head and tell it to pay more attention during the next round of flying lessons.
As for the scent issue – birds just don't smell too well. A few species are an exception, but chances are vastly greater that the little chirping ball of fluff won't suffer if you need to move it to the other side of the fence from where your dog plays. Plus, its parents have invested way too much time and energy raising it to just scoot off at the first opportunity, no matter how the little guy smells.