By “Fitness Instructor” I think you mean “Physical Therapist” (and definitely not a Chiropractor). In the US, a fitness instructor can be literally anyone who runs an aerobics class, while a physical therapist actually has medical training.
In my (limited) experience, physical therapists tend to have much broader recommendations. Like a PT might tell you to walk an hour a day, but a trainer might recommend a specific kind of crunch that targets the actual muscles in question.
And to OP's point, PTs are very much ingrained in the US medical system and consuming their services can be a pain in itself.
But the guys who get professional athletes back on the field every week are for the most part just personal trainers with a master's level education in sports science. THOSE are the guys you want to help your back recover.
My wife had back pain due to a disfigured vertebrae. That’s something they do not want to operate in until every other option is exhausted. Much of her pain and numbness is caused by imbalanced muscle development from a lifetime of incorrect posture and movements that compensated for the defective vertebrae. She’s worked with both a Physical Therapist and a Trainer to improve her strength and how she moves to the point that she is pain free 90% of the time. Both were referred to her by her doctors. They’re not part of a PT chain or gym.
Kinesiology is the study of how the body moves. While the largest target audience for that is going to be people looking for a standard gym fitness trainer, the higher degrees are wasted on that sort of thing and are better used to restore the range of motion of an elbow after a car accident.
Personally, I had a debilitating shoulder injury, couldn't put any weight on my right arm at all, and one of my yoga teachers put me on the path of fixing it up. Same with a low back injury, I couldn't even sit at one point and she helped fix me.
I'd 100% recommend someone with back pain visit a highly trained yoga or Pilates teacher. Some Pilates studios even take health insurance, since some are considered PT.
For my shoulder the main thing that worked was getting into the habit of doing pull-ups and stretching out my pec minor. Anytime I neglect pull-ups for a while the discomfort will creep back in. I probably should also buy a split keyboard.
But yeah, they can be literally anyone. A good one understands simple (bio)machines and pays close attention to how a body moves AND is a good teacher.
Edit: "A PT will get you to functional, a fitness instructor will get you to capable"