Yes, we all have different philosophies and while it is fine to discuss, I honestly don't see why people get fanatic about things.
Cuddles, play and praise are dished out liberally and I look at each of my dogs and tailor my training based on what works for that particular dog.
For me and my dogs, corrections are no bad thing. It is teaching them boundaries and helps them feel secure. They are happy, engaging dogs and i think it is because they are not stressed about anything...they understand their boundaries and that we control the resources. It relaxes them.
Of course it depends on the nature of your dogs. And also what you do with them. It the owner feeds dogs kibble, has them on leash most of the time and keep them in a crate and takes them out to 'train' them to dance and perform tricks for you, then maybe treats for all issues works, given the limited exposure these dogs have.
In our case the dogs get butter, meat and bones as a matter of course in their normal meals, are out off leash pretty much all the time and are never crated as they absolutely love their freedom to be out sniffing around for rabbits and rolling in deer poo in the land.
My girl dog is my gardening helper, she digs holes for me when I ask her to, so I can plant stuff. Never had an issue with them tearing up my garden or eating a plant or running off the land. They know their boundaries and are happy and relaxed
Since we give our dogs a lot of freedom, we expect a lot of good behaviour and use a wide range of training to get that. It all comes down to common sense, doing right by your dogs and not being afraid of them.