Tracy, I understand where you are coming from, but let me explain in more detail.
When I work with my Rottie, and he does a command wrongly, I give him an "ahhh" as a correction, as he has learnt to associate that word with negativity.
Then I ask him to heel, walk briskly for about 3-5 paces then begin with what I was doing again.
The moment he begins his heel, I go nuts with verbal praises, such as "Good boy", "That's a good heel", "Come on boy" all the while patting my left thigh to let him associate that with heel. Remember to raise the inflection on your last word, this lets the dog knows that it is a positive reinforcement/encouragement. Dogs, as I have been told, only recognise the final inflection in the commands, thus, sit = bit = fit, etc. The way you say the command will also affect how fast the dog learns.
The reason physical contact is avoided is because, as you said, dogs thrive on physical contact. During such a moment, if he obeys your heel and you pat him, you will distract your dog unnecessarily. Rather just the verbal praises would be enough to keep him going until you think you want to end the session. To keep his attention and keep the training positive, heaping verbal praises and encouragement is sufficient. I think the same would apply with food, this would distract the dog from his purpose at hand. I am sure that there are ways in which to work with a dog with either patting and/or food, but the way I have worked with my Rottie over a year resulted in him looking earnestly to my face waiting for his commands, as opposed to working for a reward, just my experience.
Remember to keep training sessions short too, probably 3 or 4 10-15 minute stints rather than 1 hour sessions once a day.
Once the session is over, I give my dog a big hug and all the patting and scratching he wants. Plus, whenever the session is over and I remove the collar, I give him the command "Free" which lets him know he can go do whatever he wants.
Regards,
TH