Do you think you can tell if a health care worker is just going through the motions, not doing it lovingly?

Yes I can. I have had only a small percentage who didn't treat me properly. Most treat me like family.

"Lovingly" isn't required, "professionally and diligently" is. A doctor is usually more dedicated to his/her skill than to the patient - the well-being of the patient in their eyes is a successful outcome from the treatment. A nurse who doesn't "care" about their patient, however, is in the wrong profession. I've met a few. VERY few.

I am fine with going through the motions as long as the motions are correctly done. 

Yes, I can tell.  Over the years I have come across healthcare "workers" who clearly were only there for a paycheck.  I ran across one such person a few years ago when I had to go to the Emergency Room for heart issues (and he called himself a doctor). 

Treating a patient "lovingly" can get one a meeting with HR.  They should treat people with patience and dignity.