I'd like to start of by saying I'm a scientist - not a hobbyist. I don't anthropomorphize my pets/specimens.
The short answer is? They're both right. Can you tame a savannah by simply luring it to you over time, using the wild animal approach? Yes, absolutely but it takes a lot of time, and even very small mistakes can prolong the process, or ruin it entirely.
Can you tame a savannah monitor simply by forcehandling it? Again, absolutely. I have two savannah monitors, and both have become hand time via forcehandling. (One is 17" STL, the other is just shy of 4' total length, both are (believed to be) females)
The problems that sources like savannahmonitor.org claim to have with the forcehandling approach, i.e. that it makes them stop eating, seems to be some insane 1/1000 anomaly. I have dozens of friends and colleagues that have owned a variety of varanids and crocodylians, and I have never once had any of them give me a first or even second-hand account of forcehandling stressing a monitor to death. One of my friends has a 3 and a half foot long male with a bullet hole that passed through the rib cage, entering next to the spine just posterior to the left scapula, and exiting under the armpit on the right side. It eats fine, although it has a very slow gait for a varanid. My point is, these creatures are extremely durable, and have an intensely strong will to live. If one does go off of food, it is likely because of extraordinarily poor husbandry, disease, or parasites. I have only had my monitors turn down food once, and that was when I experimented with freeze dried insects.
Now. I personally have only dealt with animals that weren't excessively defensive when I acquired them. Talking to my friends, colleagues, and professors, I have identified 5 basic types of Varanid personalities.
1. The Sycophant: These are the rarest types, these are the ones that genuinely seem to crave human attention, and threat displays are extraordinarily rare. The taming is basically done for you, and they're basically very large bearded dragons.
2. The Cool Kid: When presented with forcehandling, they will basically sit there and let it happen. If they are closing their eyes, it is because they are scared, and actually The Coward which I will describe later. An animal lying still in your hands or on your lap, with its eyes open and looking around is of this type.
3. The Coward: These view escape as their only viable option. They will play dead, or run away, but will rarely if ever hiss, and probably never bite outside of a feeding time mishap. My eldest monitor is/was of this variety. This sounds like what you have, and I assure you that forcehandling is fine.
4. The Bully: Similar to the coward, they will rarely if ever bite, but they will do everything in their power to make you think they will. They will hiss, and tail lash, and puff up, and do everything else to generate a threat display. They are however, bluffing and won't likely follow through. My second monitor was of this variety, and she is doing fine. She did finally bite me once and got a mouthful of vinegar: She has not done it since, and has finally started behaving properly. She takes food, is active, and no longer generates a threat display.
5. The asshole: These are the nightmares of the varanid community. Usually adult or juvenile males that were wild caught and mistreated, they will bite and scratch and tail whip and hiss and shit all over you at every opportunity. Forcehandling IS THE ONLY OPTION in this case, but you need to take special precautions. I helped take care of a friend's monitor that had this disposition, and I can give you a few tips. The obvious ones are to wear gloves. They want you to leave them alone, and they think that biting and stuff will make you do so. If it works, you're training them to be assholes and you need to stop it. I designed a special way of making biting particularly unpleasant: I wear too sets of gloves. The outer glove is a standard gardening glove, and underneath that I wear a knit one-size-fits-all glove absolutely soaked in vinegar. The vinegar won't soak through on its own, but once the savannah monitor clamps down it forces small amounts of the liquid through and into its mouth, and the taste causes them to release. These monitors are a challenge, but it is a challenge that can be overcome with persistence and a small degree of bravery.
