Lane (puppymill rescue) will probably never be fully housebroken. She certainly has no qualms about living where she's relieved herself.
I've just somewhat accepted it. After watching your dog try to bury (rubbing nose over and over on the carpet or tile) her urine, feces and spit up the same way she would try to bury her food when we first rescued her, it literally breaks your heart.
Living in a high-rise building on the 14th floor makes it harder to take her out every hour, so we've always used pee pads. I'm hopeful when we get a house with a yard she'll have more success, but I have a feeling she will always mark her territory indoors and out and submissively urinate when she meets larger dogs at the very least.
I call it marking because she loves to do the quarter sized spots. She doesn't have a medical issue, so I believe it to be marking. We are definitely on a schedule where I take her to the pad at regular intervals which seems to have helped, and we have a huge celebration dance complete with treat every time. I know she knows she has done something good, because she'll race to the kitchen trotting with her tail up and chest puffed out like she just won Westminster (that's the over 7 lb, floppy ear division, naturally) to claim her treat. All Rory has to do is hear me start into the Lane cheer for a good potty and she beats us all into the kitchen. When I catch her in the act (still squatting) of a mistake, I make an "ah, ah" noise, but she literally doesn't seem to connect what I'm scolding her for - you also have to be very careful how you correct Lane because she can be a bit timid and revert to extremely fearful from just a stern "no, Lane!", which is why I use the "ah, ah, ah" with a clap now.
In a new place, she just doesn't "get it" enough not to just squat wherever she wants to, and it seems like she is that way sometimes at home too - I don't know why. I've trained Lane the exact same way that I trained Rory (who I got as a puppy) and she definitely knows to use the pad and will seek it out wherever we are. My only issue with Rory is that sometimes she walks off the pad before the poop has finished dropping. I should probably take out stock in Nature's Miracle.
I don't think it's fair to say it's lazy or a lack of training issue. I spend a lot of time clicker training with Rory and Lane, and Lane is much slower to catch on to things than Rory is. They get lots and lots of exercise, where I let them stop and mark every foot for the first bit before we really start walking. All that being said, it's been over 2.5 years that I've had Lane - I'm not sure what is going to make her "get it" 100%.
ETA: When I take Lane to others' homes or we visit family, after I take her to potty, I put her in a pair of panties with a liner in it. I don't think it's fair to let your dog pee and poop all over someone's house and laugh it off or anything.