We've had a lovely 6 month old chihuahua x for a couple of weeks now. His previous owner insisted that he is housetrained - never had any problems with him, apparently 
He wees and poos wherever he happens to be standing when he needs to go. We've tried the standard advice of taking him out regularly (every 30 to 45 minutes) and staying with him until he goes then giving him lots of praise/treats. He couldn't care less about either and more often than not will empty out and wander off, ignoring both the praise and the treat. Still wees in the house within minutes of coming back inside.
So, we moved on to tethering. Made no difference. Last night I took him out for a wee, watched him "assume the position", brought him back inside. Within 10 minutes there was wee on the floor right beside my foot.
He sleeps in a crate overnight and holds his bladder perfectly fine. Otherwise it's a free-for-all. He even wees beside the spot where we feed him if he happens to be standing there when he feels the urge. Catching him in the act and interrupting him with a sharp noise followed immediately by being put on the grass doesn't do squat. It's like there's something missing in his brain, the bit able to make the connection needed. He's been checked by a vet and has no medical reason for this.
We are at the point of not being able to let him inside at all unless he's in his crate. It's not a problem here as it's quite warm and he's inside in his crate overnight, but I have to wonder what's the point of having a dog that can't be part of the family. Even having him outside without being trained can't go on for long because he goes all over the concrete. He's going to have to be rehomed if we can't get this under control soon.