I actually heard this on overnight news while I was half awake, and then wasn't sure if I had dreamed it. But no, I looked into it and found out it is indeed true.
I don't know exactly when this was implemented, but it couldn't have been too long ago, as it only made the news last night. The St. Louis Airport has added two tiny dog parks to its terminals. I don't know if each is 400 square feet, or if they total 400 square feet together -- what I read was unclear -- but I hope it's the former.
At the Main Terminal, outside Exit MT-6 there is a fenced area with synthetic turf. At the East Terminal, outside baggage claim, there is real grass and a tree! Both areas have benches, fire hydrants, and plastic mitts for owners to use to clean up after their dogs.
What I heard and read suggested that dogs could "romp" and called them dog parks, and I think meant that dogs could be off-leash. I would certainly want to see how very secure that fencing is before I would let a dog off-leash at an airport, but at least it's somewhere to take a dog for a potty break before or after a flight. I don't fly my dogs, but I know people who do, and that's often a big problem.
The airport spokesperson said that other airports have made similar improvements, though he didn't give any details. So I don't know if this idea has come to an airport near you, or one to which you'll be traveling, but it's a step in the right direction. I mean, Seattle-Tacoma airport has a meditation room. A dog park doesn't seem like such a wild idea.