They don't ALWAYS do well, sure, but...mine did.
I caught my first gray in a friend's swimming pool back in 2005. He was relatively young at the time. Not a froglet, but a small, young frog. The stress of silly younger me playing with him daily didn't cause him to die. Nor did my moving to a different climate (I caught him in Virginia, and then moved to Minnesota 2 years later). He died in January.
I got my second gray (friend caught her) in August 2006? 2007? She only lived until 2009, but she was definitely older than my male.
Personally, I have no qualms about catching things wild. I grew up in the sticks and loved chasing down and snatching up little critters, though the frog was the first one I didn't release.
Grays are pretty hardy little stinkers. I mean, if it lives in such a wide range of temperatures, and can handle below freezing temps in the winter, and handle being messed with, I'd say it's got a good chance of making a GREAT wild caught pet. Shame they're not big in pet stores, they're great pets! And cute too.
But yeah, like Sniffer suggested, check rain barrels, check kiddie pools, check man-made ponds, check your backyard. They'll sometimes hop around.