It's definitely an old wives tale that "if you touch a baby animal it will be abandoned by the mother." I wonder if you have a 'bird rescue' person you could ask about the bird, JIC, if it is injured though. I'm surprised you could catch the baby bird, normally they are pretty fast. If you can catch it again without stressing it out too much, just pick it up - gently - and place it back in the nest. Reason is that it is vulnerable to predators on the ground. But if you think it is safe from cats and other predators, you could always just leave it. Make no mistake, mommy is watching her baby! (You may even see her fly down to her baby.)
Again, don't even worry about touching the bird. You can wash your hands afterwards of course. But other than that...no worries!