I've been where I had a 6-pack even when slouching! Not recommended, it takes body fat of less than 10%!
I think the binder may encourage you to breathe using your belly more. Belly breating is done more in bicycle racing, there are pics out there of skinny bike guys with what looks like a beer belly, crouched over the bike lol. Running discourages belly breathing and encourages chest breathing.
I feel like I've got a bit of a belly too and I think it's because of riding a motorcycle - no not that we bikers like beer, which of course we do! It's because while riding air likes to sneak in under the bottom of the jacket, and one's shirt likes to come untucked, and pushing out the belly stops these things.
I have only used sports bras myself no binders, I'd like to try one sometime but they cost $$ so that's a problem for me. I dunno if I'd like using a binder or not. They sound uncomfortable.