When grabbing video in a public setting (your child’s baseball game), downloading YouTube video or filming the game of the week off of your big screen TV with your smartphone, you must respect copyright law. Still, even copyrighted material is subject to fair use. Interpretation can be complicated. As the US Copyright Office states themselves: “The distinction between what is fair use and what is infringement in a particular case will not always be clear or easily defined.”
Major League Baseball (MLB), for example, owns all footage that happens ‘between the lines’ of MLB games. They also own the logos on the jerseys. They are aggressive in defending their copyrights. While instructional usage (comparing your son to a MLB player on PowerChalk) might be within fair use, using that same clip on an instructional CD would not be.
Also from the Copyright Office:
“Even if the content borrowed falls under fair use, the copyright owner can contest that usage and a defense would cost thousands of dollars. There are few blanket statements that can be made regarding Fair Use. Users should make their own judgements and when in doubt, “consider avoiding the use of copyrighted material unless you are confident that the doctrine of fair use would apply to the situation.”